{{Use dmy dates|date=January 2015}}
[[File:Graphen.jpg|thumb|Graphene is an atomic-scale [[hexagonal lattice]] made of [[carbon]] atoms.]]
'''Graphene''' {{IPAc-en|ˈ|g|r|æ|f|iː|n}}<ref name=camdic/> is a [[allotropes of carbon|form]] of [[carbon]] consisting of a single layer of atoms arranged in [[2D Materials|two-dimensional]] [[hexagonal lattice|honeycomb lattice]].<ref name=geim2007/><ref name=peres2009/>  The name is a contraction of "graphite" and the suffix [[-ene]], reflecting the fact that the [[graphite]] allotrope of carbon consists of stacked graphene layers.<ref name=boehm1962a/><ref name=boehm1994/> 

Each atom in a graphene sheet is connected to its three nearest neighbors by a [[σ-bond]], and contributes one [[electron]] to a [[conduction band]] that extends over the whole sheet.  This is the same type bonding seen in [[carbon nanotube]]s and [[polycyclic aromatic hydrocarbon]]s, and (partially) in [[fullerene]]s and [[glassy carbon]].<ref name=zdet2015/><ref name=harris2018/>  These conduction bands make graphene a [[semimetal]] with unusual [[electronic properties of graphene|electronic properties]] that are best described by theories for massless relativistic particles.<ref name=geim2007/> Charge carriers in graphene show linear, rather than quadratic, dependence of energy on momentum, and field-effect transistors with graphene can be made that show bipolar conduction. Charge transport is [[ballistic conduction|ballistic]] over long distances; the material exhibits large [[quantum oscillations (experimental technique)|quantum oscillations]] and large and nonlinear [[diamagnetism]].<ref name=lizhi2015/> Graphene conducts heat and electricity very efficiently along its plane.  The material strongly absorbs light of all visible wavelengths,<ref name=nair2008/><ref name=zhu2014/> which accounts for the black color of graphite; yet a single graphene sheet is nearly transparent because of its extreme thinness.  The material is also about 100 times stronger than would be the strongest steel of the same thickness.<ref name=lee2008/><ref name=cao2020/>

[[File:Graphene visible.jpg|right|thumb|Photograph of a suspended graphene membrane in transmitted light. This one-atom-thick material can be seen with the naked eye because it absorbs approximately 2.3% of light.<ref name=zhu2014/> <ref name=nair2008/>]]
Scientists have theorized about graphene for decades. It has likely been unknowingly produced in small quantities for centuries, through the use of pencils and other similar applications of graphite. It was originally observed in [[electron microscope]]s in 1962, but only studied while supported on metal surfaces.<ref name=boehm1962a/> The material was later rediscovered, isolated and characterized in 2004 by [[Andre Geim]] and [[Konstantin Novoselov]] at the [[University of Manchester]],<ref name=novo2004/><ref name=aps2009/> who were awarded the [[Nobel Prize in Physics]] in 2010 for their research on the material. High-quality graphene proved to be surprisingly easy to isolate.

The global market for graphene was $9 million in 2012,<ref name=azon2014/> with most of the demand from research and development in semiconductor, electronics, [[electric battery|electric batteries]],<ref name=mrmak2014/> and [[composite material|composites]]. In 2019, it was predicted to reach over $150 million by 2021.<ref name=prnews2019/>

The [[International Union of Pure and Applied Chemistry|IUPAC]] recommends use of the name "graphite" for the three-dimensional material, and "graphene" only when the reactions, structural relations or other properties of individual layers are discussed.<ref name=IUPAC2009/> A narrower definition, of "isolated or free-standing graphene" requires that the layer be sufficiently isolated from its environment,<ref name=geim2009a/> but would include layers suspended or transferred to [[silicon dioxide]] or [[silicon carbide]].<ref name=ried2009/>

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==History==
[[File:Nobelpriset i fysik 2010.png|thumb|A lump of [[graphite]], a graphene [[transistor]], and a [[tape dispenser]]. Donated to the [[Nobel Museum]] in Stockholm by [[Andre Geim]] and [[Konstantin Novoselov]] in 2010.]]

===Structure of graphite and its intercalation compounds===
In 1859 [[Sir Benjamin Collins Brodie, 2nd Baronet|Benjamin Brodie]] noted of the highly [[lamella (materials)|lamellar]] structure of thermally reduced [[graphite oxide]].<ref name=geim2012/><ref name=brod1859/>  In 1916, [[Peter Debije]] and [[P. Scherrer]] determined the structure of graphite by [[powder diffraction|powder X-ray diffraction]].<ref name=deb1916/><ref name=fried1913/><ref name=hull1917/> The structure was studied in more detail by V. Kohlschütter and P. Haenni in 1918, who also described the properties of [[graphene oxide paper|graphite oxide paper]].<ref name=kohl1918/> Its structure was determined from single-crystal diffraction in 1924.<ref name=bern1924/><ref name=hass1924/>

The theory of graphene was first explored by [[P. R. Wallace]] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out in 1984 by [[Gordon Walter Semenoff]],David P. DiVincenzo, and Eugene J. Mele.<ref name=divi1984/> Semenoff emphasized the occurrence in a magnetic field of an electronic [[Landau level]] precisely at the [[Dirac point]]. This level is responsible for the anomalous integer [[quantum Hall effect]].<ref name=novo2005/><ref name=gusy2005/><ref name=zhang2005/>

===Observations of thin graphite layers and related structures===

[[Transmission electron microscopy]] (TEM) images of thin graphite samples consisting of a few graphene layers were published by G. Ruess and F. Vogt in 1948.<ref name=ruess1948/>)  Eventually, single layers were also observed directly.<ref name=meyer2007/> Single layers of graphite were also observed by [[transmission electron microscopy]] within bulk materials, in particular inside soot obtained by chemical exfoliation.<ref name=harris2018/>

In 1961-1962, [[Hanns-Peter Boehm]] published a study of extremely thin flakes of graphite, and coined the term "graphene" for the hypothetical single-layer structure.<ref name=boehm1962b/>  This paper reports graphitic flakes that give an additional contrast equivalent of down to ~0.4 [[nanometre|nm]] or 3 atomic layers of amorphous carbon. This was the best possible resolution for 1960 TEMs. However, neither then nor today it is possible to argue how many layers were in those flakes. Now we know that the TEM contrast of graphene most strongly depends on focusing conditions.<ref name=meyer2007/> For example, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known way is to analyse relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are probably given in refs. 24 and 26 of Geim and Vovoselov's 2007 review.<ref name=geim2007/>

Starting in the 1970s, [[C. Oshima]] and others described single layers of carbon atoms that were grown epitaxially on top of other materials.<ref name=oshi1997/><ref name=forb1998/> This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp<sup>2</sup>-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer between the two materials, and, in some cases, hybridization between the [[d-orbital]]s of the substrate atoms and π orbitals of graphene; which significantly alter the electronic structure compared to that of free-standing graphene.

The term "graphene" was used again in 1987 to describe single sheets of graphite as a constituent of [[graphite intercalation compound]]s,<ref name=mour1987/> which can be seen as crystalline salts of the intercalant and graphene. It was also used in the descriptions of [[carbon nanotube]]s by [[R. Saito]] in 1992,<ref name=saito1992/> and of polycyclic aromatic hydrocarbons in 2000 by [[S. Wang]] and others.<ref name=wang2000/>

Efforts to make thin films of graphite by mechanical exfoliation started in 1990.<ref name=geim2008/>
Initial attempts employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.<ref name=geim2007/> 

In 2002, [[Robert B. Rutherford]] and [[Richard L. Dudman]] filed for a [[patent]] in the US on a method to produce graphene by repeatedly peeling off layers from a graphite flake adhered to a substrate, achieving a graphite thickness of {{convert|0.00001|inch|m|abbr=off|lk=on}}. The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast.<ref name=ruth2002/>  

Another patent was filed in the same year by  [[Bor Z. Jang]] and [[Wen C. Huang]] filed a [[patent]] in the US for a method to produce graphene, based on exfoliation followed by attrition.<ref name=jang2002/>

===Full isolation and characterization===

[[File:Nobel Prize 2010-Press Conference KVA-DSC 8009.jpg|thumb|Andre Geim and Konstantin Novoselov at the Nobel Laureate press conference, [[Royal Swedish Academy of Sciences]], 2010.]]
Graphene was properly isolated and characterized in 2004 by [[Andre Geim]] and [[Konstantin Novoselov]] at the [[University of Manchester]].<ref name=novo2004/><ref name=aps2009/>  They pulled graphene layers from graphite with a common [[adhesive tape]] in a process called either micromechanical cleavage or the [[Scotch tape]] technique.<ref name=manch2014/> The graphene flakes were then transferred onto thin [[silicon dioxide]] (silica) layer on a [[silicon]] plate ("wafer"). The silica electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. 

This work resulted in the two winning the [[Nobel Prize in Physics]] in 2010 "for groundbreaking experiments regarding the two-dimensional material graphene."<ref name=ukiop2010/><ref name=nobel2013/><ref name=manch2014/>  Their publication, and the surprisingly easy preparation method that they described, sparked a "graphene gold rush".  Research expanded and split off into many different subfields, exploring different exceptional properties of the material — quantum mechanical, electrical, chemical, mechanical, optical, magnetic, etc..

===Exploring commercial applications===

Since the early 2000s, a number of companies and research laboratories have been working to develop commercial applications of graphene.  In 2014 a [[National Graphene Institute]] was established with that purpose at the University of Manchester, with a 60 million [[British pound|GBP]] initial funding.<ref name=manch2014f/>  In [[North East England]] two commercial manufacturers, [[Applied Graphene Materials]]<ref name=burn2014/> and [[Thomas Swan Limited]]<ref name=gibs2014/><ref name=thej2014/> have begun manufacturing. [[FGV Cambridge Nanosystems]],<ref name=canew2015/> is a large scale graphene powder production facility in [[East Anglia]].

==Structure==
===Bonding===
[[File:Carbon hybrid orbitals - from s+px,py,pz to sp²+pz.svg|thumb|250x250px|Carbon orbitals 2s, 2p<sub>x</sub>, 2p<sub>y</sub> form the hybrid orbital sp<sup>2</sup> with three major lobes at 120°. The remaining orbital, p<sub>z</sub>, is sticking out of the graphene's plane.]]
[[File:Graphene - sigma and pi bonds.svg|thumb|249x249px|Sigma and pi bonds in graphene. Sigma bonds result from an overlap of sp<sup>2</sup> hybrid orbitals, whereas pi bonds emerge from tunneling between the protruding pz orbitals.]]
Three of the four outer-[[electron shell|shell]] electrons of each atom in a graphene sheet occupy three sp<sup>2</sup> [[orbital hybridization|hybrid orbitals]] – a combination of orbitals s, p<sub>x</sub> and p<sub>y</sub> — tha are shared with the three nearest atoms, forming [[σ-bond]]s. The length of these [[carbon–carbon bond|bonds]] is about 0.142 [[nanometer]]s.<ref name=heyr2008/><ref name=coop2012/><ref name=felix2013/>

The remaining outer-shell electron occupies a p<sub>z</sub> orbital that is oriented perpendicularly to the plane.  These orbitals hybridize together to form two half-filled [[conduction band|bands]] of free-moving electrons, π and π∗, which are responsible for most of graphene's notable electronic properties.<ref name=coop2012/> Recent quantitative estimates of aromatic stabilization and limiting size derived from the enthalpies of hydrogenation (ΔH<sub>hydro</sub>) agree well with the literature reports.<ref name=dixit2019/>

Graphene sheets stack to form graphite with an interplanar spacing of {{convert|0.335|nm|angstrom|abbr=on|lk=on}}.<ref name=coop2012/>

Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref name=kasu2002/> However, unlayered graphene with only (hk0) rings has been found in the core of [[presolar grains|presolar]] graphite onions.<ref name=bern1996/> TEM studies show faceting at defects in flat graphene sheets<ref name=fraun2002/> and suggest a role for two-dimensional crystallization from a melt.

===Geometry===
[[File:Graphene SPM.jpg|thumb|upright|[[Scanning probe microscopy]] image of graphene|alt=]]

The hexagonal lattice [[atomic structure|structure]] of isolated, single-layer graphene can be directly seen with transmission electron microscopy (TEM) of sheets of graphene suspended between bars of a metallic grid<ref name=meyer2007/>  Some of these images showed a "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,<ref name=geim2007/><ref name=carl2007/><ref name=faso2007/> or may originate from the ubiquitous dirt seen in all TEM images of graphene.  [[Photoresist]] residue, which must be removed to obtain atomic-resolution images, may be the "[[adsorbate]]s" observed in TEM images, and may explain the observed rippling.{{cn|date=August 2020}}

The hexagonal structure is also seen in [[scanning tunneling microscope]] (SEM) images of graphene supported on silicon dioxide substrates<ref name=ishi2007/>  The rippling seen in these images is caused by conformation of graphene to the subtrate's lattice, and is not intrinsic.<ref name=ishi2007/>

===Stability===

[[Ab initio quantum chemistry methods|Ab initio calculations]] show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm and becomes the most stable [[fullerene]] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=shen2006/>


==Properties==

===Chemical===
Graphene has a theoretical [[specific surface area]] (SSA) of {{val|2630 |ul=m2 |up=g}}. This is much larger than that reported to date for carbon black (typically smaller than {{val|900 |ul=m2 |up=g}}) or for carbon nanotubes (CNTs), from ≈100 to {{val|1000 |ul=m2 |up=g}} and is similar to [[activated carbon]].<ref>{{cite journal |doi=10.1126/science.1246501 |pmid=25554791 |title=Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage |journal=Science |volume=347 |issue=6217 |page=1246501 |year=2015 |last1=Bonaccorso |first1=F. |last2=Colombo |first2=L. |last3=Yu |first3=G. |last4=Stoller |first4=M. |last5=Tozzini |first5=V. |last6=Ferrari |first6=A. C. |last7=Ruoff |first7=R. S. |last8=Pellegrini |first8=V. |bibcode=2015Sci...347...41B}}</ref>

Graphene is the only form of carbon (or solid material) in which every atom is available for chemical reaction from two sides (due to the 2D structure). Atoms at the edges of a graphene sheet have special chemical reactivity. Graphene has the highest ratio of edge atoms of any [[allotrope]]. Defects within a sheet increase its chemical reactivity.<ref name="Denis">{{cite journal |last1=Denis |first1=P. A. |last2=Iribarne |first2=F. |title=Comparative Study of Defect Reactivity in Graphene |doi=10.1021/jp4061945 |journal=Journal of Physical Chemistry C |volume=117 |pages=19048–19055 |year=2013 |issue=37}}</ref> The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below {{convert|260|C|K|sigfig=2}}.<ref name="Yamada3">{{cite journal |last1=Yamada |first1=Y. |last2=Murota |first2=K |last3=Fujita |first3=R |last4=Kim |first4=J |s2cid=12628957 |title=Subnanometer vacancy defects introduced on graphene by oxygen gas |doi=10.1021/ja4117268 |pmid=24460150 |journal=Journal of the American Chemical Society |volume=136 |issue=6 |pages=2232–2235 |year=2014 |display-authors=etal}}</ref> Graphene burns at very low temperature (e.g., {{convert|350|C|K|sigfig=2}}).<ref name="Eftekhari">{{cite journal |last1=Eftekhari |first1=A. |last2=Jafarkhani |first2=P. |title=Curly Graphene with Specious Interlayers Displaying Superior Capacity for Hydrogen Storage |doi=10.1021/jp410044v |journal=Journal of Physical Chemistry C |volume=117 |pages=25845–25851 |year=2013 |issue=48}}</ref> Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. However, determination of structures of graphene with oxygen-<ref name="Yamada1">{{cite journal |last1=Yamada |first1=Y. |last2=Yasuda |first2=H. |last3=Murota |first3=K. |last4=Nakamura |first4=M. |last5=Sodesawa |first5=T. |last6=Sato |first6=S. |title=Analysis of heat-treated graphite oxide by X-ray photoelectron spectroscopy |doi=10.1007/s10853-013-7630-0 |journal=Journal of Materials Science |volume=48 |pages=8171–8198 |year=2013 |issue=23|bibcode=2013JMatS..48.8171Y }}</ref> and nitrogen-<ref name="Yamada2">{{cite journal |last1=Yamada |first1=Y. |last2=Kim |first2=J. |last3=Murota |first3=K. |last4=Matsuo |first4=S. |last5=Sato |first5=S. |title=Nitrogen-containing graphene analyzed by X-ray photoelectron spectroscopy |doi=10.1016/j.carbon.2013.12.061 |journal=Carbon |volume=70 |pages=59–74 |year=2014}}</ref> functional groups requires the structures to be well controlled.

In 2013, [[Stanford University]] physicists reported that single-layer graphene is a hundred times more chemically reactive than thicker sheets.{{vague|thicker sheets of what? Graphene is only one atom thick, so is the comparison with graphite? |date=June 2014}}<ref>{{cite news |url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected |work=Phys.org |date=1 February 2013}}</ref>

Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as [[hydrocarbon]]s. Bombarded with pure carbon atoms, the atoms perfectly align into [[hexagon]]s, completely filling the holes.<ref name=zan2012/><ref name=puiu2012/>

===Electronic===
{{main|Electronic properties of graphene}}

[[File:Electronic band structure of graphene.svg|thumb|306x306px|Electronic band structure of graphene. Valence and conduction bands meet at the six vertices of the hexagonal Brillouin zone and form linearly dispersing Dirac cones.]]
Graphene is a zero-gap [[semiconductor]], because its [[Conduction band|conduction]] and [[valence bands]] meet at the Dirac points. The Dirac points are six locations in [[momentum space]], on the edge of the [[Brillouin zone]], divided into two non-equivalent sets of three points. The two sets are labeled K and K'. The sets give graphene a valley degeneracy of {{nowrap |1=''gv'' = 2}}. By contrast, for traditional semiconductors the primary point of interest is generally Γ, where momentum is zero.<ref name=coop2012/> Four electronic properties separate it from other [[condensed matter]] systems.

However, if the in-plane direction is no longer infinite, but confined, its electronic structure would change. They are referred to as [[graphene nanoribbon]]s. If it is "zig-zag", the bandgap would still be zero. If it is "armchair", the bandgap would be non-zero (see figure).

Graphene's hexagonal lattice can be regarded as two interleaving triangular lattices. This perspective was successfully used to calculate the band structure for a single graphite layer using a tight-binding approximation.<ref name=coop2012/>

====Electronic spectrum====

Electrons propagating through graphene's honeycomb lattice effectively lose their mass, producing [[quasi-particle]]s that are described by a 2D analogue of the [[Dirac equation]] rather than the [[Schrödinger equation]] for spin-{{frac|1|2}} particles.<ref name="Castro" /><ref name="E-Phonon">{{cite book |url={{google books |plainurl=yes |id=ammoVEI-H2gC}} |last1=Charlier |first1=J.-C. |last2=Eklund |first2=P.C. |last3=Zhu |first3=J. |last4=Ferrari |first4=A.C. |title=Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes |work=Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications |editor1-first=A. |editor1-last=Jorio |editor2-first=G. |editor2-last=Dresselhaus and |editor3-first=M.S. |editor3-last=Dresselhaus |location=Berlin/Heidelberg |publisher=Springer-Verlag |year=2008}}</ref>

====Dispersion relation====

[[File:Graphene and Dirac Cones.ogv|thumb |Electronic band structure and Dirac cones, with effect of [[doping (semiconductor)|doping]]{{cn|date=July 2020}}|220x220px]]

The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005, by Geim's group and by [[Philip Kim]] and [[Yuanbo Zhang]].  This effect provided direct evidence of graphene's theoretically predicted [[Berry's phase]] of massless [[Dirac fermion]]s and the first proof of the Dirac fermion nature of electrons.<ref name=novo2005/><ref name=zhang2005/> These effects had been observed in bulk graphite by [[Yakov Kopelevich]], [[Igor A. Luk'yanchuk]], and others, in 2003-2004.<ref name=kope2003/><ref name=luky2004/>.

When the atoms are placed onto the graphene hexagonal lattice, the overlap between the ''p''<sub>z</sub>(π) orbitals and the ''s'' or the ''p''<sub>x</sub> and ''p''<sub>y</sub> orbitals is zero by symmetry. The ''p''<sub>z</sub> electrons forming the π bands in graphene can therefore be treated independently. Within this π-band approximation, using a conventional [[tight-binding]] model, the [[dispersion relation]] (restricted to first-nearest-neighbor interactions only) that produces energy of the electrons with wave vector ''k'' is<ref name="Semenoff" /><ref name="Wallace">{{cite journal |last=Wallace |first=P.R. |s2cid=53633968 |title=The Band Theory of Graphite |doi=10.1103/PhysRev.71.622 |journal=Physical Review |volume=71 |year=1947 |pages=622–634 |bibcode=1947PhRv...71..622W |issue=9}}</ref>

:<math>E(k_x,k_y)=\pm\,\gamma_0\sqrt{1+4\cos^2{\tfrac{1}{2}ak_x}+4\cos{\tfrac{1}{2}ak_x} \cdot \cos{\tfrac{\sqrt{3}}{2}ak_y}}</math>

with the nearest-neighbor (π orbitals) hopping energy ''γ''<sub>0</sub> ≈ {{val|2.8 |u=eV}} and the [[lattice constant]] {{nowrap|''a'' ≈ {{val|2.46 |u=Å}}}}. The [[conduction band|conduction]] and [[valence band]]s, respectively, correspond to the different signs. With one ''p''<sub>z</sub> electron per atom in this model the valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the ''K'' point in the Brillouin zone), where there is a zero density of states but no band gap. The graphene sheet thus displays a semimetallic (or zero-gap semiconductor) character, although the same cannot be said of a graphene sheet rolled into a [[carbon nanotube]], due to its curvature. Two of the six Dirac points are independent, while the rest are equivalent by symmetry. In the vicinity of the ''K''-points the energy depends ''linearly'' on the wave vector, similar to a relativistic particle.<ref name="Semenoff">{{Cite journal |last=Semenoff |first=G. W. |title=Condensed-Matter Simulation of a Three-Dimensional Anomaly |doi=10.1103/PhysRevLett.53.2449 |journal=Physical Review Letters |volume=53 |pages=2449–2452 |year=1984 |bibcode=1984PhRvL..53.2449S |issue=26}}</ref><ref name="CBE">{{Cite journal |last1=Avouris |first1=P. |last2=Chen |first2=Z. |last3=Perebeinos |first3=V. |title=Carbon-based electronics |doi=10.1038/nnano.2007.300 |journal=Nature Nanotechnology |volume=2 |year=2007 |pmid=18654384 |issue=10 |bibcode=2007NatNa...2..605A |pages=605–15}}</ref> Since an elementary cell of the lattice has a basis of two atoms, the [[wave function]] has an effective [[Spinor|2-spinor structure]].

As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless [[Dirac equation]]. Hence, the electrons and holes are called Dirac [[fermions]].<ref name="Semenoff" /> This pseudo-relativistic description is restricted to the [[Chirality (chemistry)|chiral limit]], i.e., to vanishing rest mass ''M''<sub>0</sub>, which leads to interesting additional features:<ref name="Semenoff" /><ref name="cabra2">{{cite journal |last1=Lamas |first1=C.A. |first2=D.C. |last2=Cabra |first3=N. |last3=Grandi |title=Generalized Pomeranchuk instabilities in graphene |journal=Physical Review B |year=2009 |volume=80 |issue=7 |page=75108 |doi=10.1103/PhysRevB.80.075108 |arxiv=0812.4406 |bibcode=2009PhRvB..80g5108L}}</ref>

:<math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math>

Here ''v<sub>F</sub>'' ~ {{val |e=6 |u=m/s}} (.003 c) is the [[Fermi velocity]] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the [[Pauli matrices]], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro" />

The equation describing the electrons' linear dispersion relation is

:<math>E(q)=\hbar v_F q</math>

where the [[wavevector]] ''q'' is measured from the Brillouin zone vertex K, <math>q=\left|\mathbf{k}-\mathrm{K}\right|</math>, and the zero of energy is set to coincide with the Dirac point. The equation uses a pseudospin matrix formula that describes two sublattices of the honeycomb lattice.<ref name="CBE" />

====Single-atom wave propagation====

Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as [[high-κ dielectric]]s, [[superconductor]]s and [[ferromagnetic]]s.

====Ambipolar electron and hole transport====
[[File:Graphene - Geim - ambipolar FET.svg|thumb|221x221px|When the gate voltage in a field effect graphene device is changed from positive to negative, conduction switches from electrons to holes. The charge carrier concentration is proportional to the applied voltage. Graphene is neutral at zero gate voltage and resistivity is at its maximum because of the dearth of charge carriers. The rapid fall of resistivity when carriers are injected shows their high mobility, here of the order of 5000 cm²/Vs. n-Si/SiO₂ substrate, T=1K. <ref name=geim2007/>]]
Graphene displays remarkable [[electron mobility]] at room temperature, with reported values in excess of {{val|15000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}}.<ref name=geim2007/> Hole and electron mobilities are nearly the same.<ref name="E-Phonon" /> The mobility is independent of temperature between {{val|10 |u=K}} and {{val|100 |u=K}},<ref name=novo2005/><ref name="GiantMobility">{{cite journal |last1=Morozov |first1=S.V. |last2=Novoselov |first2=K. |last3=Katsnelson |first3=M. |last4=Schedin |first4=F. |last5=Elias |first5=D. |last6=Jaszczak |first6=J. |last7=Geim |first7=A. |title=Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer |doi=10.1103/PhysRevLett.100.016602 |journal=Physical Review Letters |volume=100 |page=016602 |year=2008 |pmid=18232798 |bibcode=2008PhRvL.100a6602M |issue=1 |arxiv=0710.5304}}</ref><ref name="E-ph">{{cite journal |last1=Chen |first1=J. H. |last2=Jang |first2=Chaun |last3=Xiao |first3=Shudong |last4=Ishigami |first4=Masa |last5=Fuhrer |first5=Michael S. |title=Intrinsic and Extrinsic Performance Limits of Graphene Devices on {{chem|SiO|2}} |doi=10.1038/nnano.2008.58 |journal=Nature Nanotechnology |volume=3 |year=2008 |pmid=18654504 |issue=4 |pages=206–9|arxiv=0711.3646 }}</ref> and shows little change even at room temperature (300 K),<ref name=geim2007/> which implies that the dominant scattering mechanism is [[defect scattering]]. Scattering by graphene's acoustic [[phonon]]s intrinsically limits room temperature mobility in freestanding graphene to {{val|200000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}} at a carrier density of {{val |e=12 |u=cm<sup>−2</sup>}}.<ref name="E-ph" /><ref name="GrapheneMC">{{cite journal |last1=Akturk |first1=A. |last2=Goldsman |first2=N. |title=Electron transport and full-band electron–phonon interactions in graphene |doi=10.1063/1.2890147 |journal=Journal of Applied Physics |volume=103 |year=2008 |bibcode=2008JAP...103e3702A |issue=5|pages=053702–053702–8 }}</ref> 

The corresponding [[resistivity]] of graphene sheets would be {{val |e=-6 |u=Ω⋅cm}}. This is less than the resistivity of [[silver]], the lowest otherwise known at room temperature.<ref name="UMDnews">[https://newsdesk.umd.edu/scitech/release.cfm?ArticleID=1621 Physicists Show Electrons Can Travel More Than 100 Times Faster in Graphene :: University Communications Newsdesk, University of Maryland] {{webarchive |url=https://web.archive.org/web/20130919083015/https://newsdesk.umd.edu/scitech/release.cfm?ArticleID=1621 |date=19 September 2013 }}. Newsdesk.umd.edu (24 March 2008). Retrieved on 2014-01-12.</ref> However, on {{chem|SiO|2}} substrates, scattering of electrons by optical phonons of the substrate is a larger effect than scattering by graphene's own phonons. This limits mobility to {{val|40000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}}.<ref name="E-ph" />

Charge transport has major concerns due to adsorption of contaminants such as water and oxygen molecules. This leads to non-repetitive and large hysteresis I-V characteristics. Researchers must carry out electrical measurements in vacuum. The protection of graphene surface by a coating with materials such as SiN, [[Poly(methyl methacrylate)|PMMA]], h-BN, etc., have been discussed by researchers. In January 2015, the first stable graphene device operation in air over several weeks was reported, for graphene whose surface was protected by [[Aluminium oxide|aluminum oxide]].<ref>{{cite journal |last=Sagade |first=A. A. |s2cid=24846431 |title=Highly Air Stable Passivation of Graphene Based Field Effect Devices |doi=10.1039/c4nr07457b |pmid=25631337 |journal=Nanoscale |volume=7 |issue=8 |pages=3558–3564 |year=2015 |display-authors=etal |bibcode=2015Nanos...7.3558S}}</ref><ref>{{cite web |url=https://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphene-devices-stand-the-test-of-time |title=Graphene Devices Stand the Test of Time|date=2015-01-22}}</ref> In 2015 [[lithium]]-coated graphene exhibited [[superconductivity]], a first for graphene.<ref>{{cite web |title=Researchers create superconducting graphene |url=http://www.rdmag.com/news/2015/09/researchers-create-superconducting-graphene |accessdate=2015-09-22|date=2015-09-09 }}</ref>

Electrical resistance in 40-nanometer-wide [[nanoribbon]]s of epitaxial graphene changes in discrete steps. The ribbons' conductance exceeds predictions by a factor of 10. The ribbons can act more like [[optical waveguide]]s or [[quantum dot]]s, allowing electrons to flow smoothly along the ribbon edges. In copper, resistance increases in proportion to length as electrons encounter impurities.<ref name="k1402">{{cite web |url=http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons |title=New form of graphene allows electrons to behave like photons |work=kurzweilai.net}}</ref><ref name="doi_12952">{{cite journal |doi=10.1038/nature12952 |pmid=24499819 |title=Exceptional ballistic transport in epitaxial graphene nanoribbons |journal=Nature |volume=506 |issue=7488 |pages=349–354 |year=2014 |last1=Baringhaus |first1=J. |last2=Ruan |first2=M. |last3=Edler |first3=F. |last4=Tejeda |first4=A. |last5=Sicot |first5=M. |last6=Taleb-Ibrahimi |first6=A. |last7=Li |first7=A. P. |last8=Jiang |first8=Z. |last9=Conrad |first9=E. H. |last10=Berger |first10=C. |last11=Tegenkamp |first11=C. |last12=De Heer |first12=W. A. |arxiv=1301.5354 |bibcode=2014Natur.506..349B}}</ref>

Transport is dominated by two modes. One is ballistic and temperature independent, while the other is thermally activated. Ballistic electrons resemble those in cylindrical [[carbon nanotube]]s. At room temperature, resistance increases abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres (1% of the former length).<ref name="k1402" />

Graphene electrons can cover micrometer distances without scattering, even at room temperature.<ref name="Castro" />

Despite zero carrier density near the Dirac points, graphene exhibits a minimum [[Electrical conductivity|conductivity]] on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon" /> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of order <math>4e^2/h</math> or greater<ref name=geim2007/> and depend on impurity concentration.<ref name="K">{{cite journal |last1=Chen |first1=J. H. |last2=Jang |first2=C. |last3=Adam |first3=S. |last4=Fuhrer |first4=M. S. |last5=Williams |first5=E. D. |last6=Ishigami |first6=M. |title=Charged Impurity Scattering in Graphene |doi=10.1038/nphys935 |journal=Nature Physics |volume=4 |pages=377–381 |year=2008 |bibcode=2008NatPh...4..377C |issue=5 |arxiv=0708.2408}}</ref>

Near zero carrier density graphene exhibits positive photoconductivity and negative photoconductivity at high carrier density. This is governed by the interplay between photoinduced changes of both the Drude weight and the carrier scattering rate.<ref>[http://www.kurzweilai.net/light-pulses-control-how-graphene-conducts-electricity Light pulses control how graphene conducts electricity]. kurzweilai.net. 4 August 2014</ref>

Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum.<ref name="K" /><ref name="ChemDoping">{{cite journal |last1=Schedin |first1=F. |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Hill |first4=E. W. |last5=Blake |first5=P. |last6=Katsnelson |first6=M. I. |last7=Novoselov |first7=K. S. |title=Detection of individual gas molecules adsorbed on graphene |doi=10.1038/nmat1967 |journal=Nature Materials |volume=6 |pages=652–655 |year=2007 |pmid=17660825 |issue=9 |bibcode=2007NatMa...6..652S|arxiv=cond-mat/0610809 }}</ref> Even for [[dopant]] concentrations in excess of 10<sup>12</sup> cm<sup>−2</sup> carrier mobility exhibits no observable change.<ref name="ChemDoping" /> Graphene doped with [[potassium]] in [[ultra-high vacuum]] at low temperature can reduce mobility 20-fold.<ref name="K" /><ref name="GrapheneCharge">{{cite journal |last1=Adam |first1=S. |last2=Hwang |first2=E. H. |last3=Galitski |first3=V. M. |last4=Das Sarma |first4=S. |title=A self-consistent theory for graphene transport |journal=Proc. Natl. Acad. Sci. USA |volume=104 |arxiv=0705.1540 |year=2007 |doi=10.1073/pnas.0704772104 |pmid=18003926 |issue=47 |pmc=2141788 |bibcode=2007PNAS..10418392A |pages=18392–7}}</ref> The mobility reduction is reversible on heating the graphene to remove the potassium.

Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum<ref>{{cite journal |first1=Hadar |last1=Steinberg |first2=Gilad |last2=Barak |first3=Amir |last3=Yacoby |title=Charge fractionalization in quantum wires (Letter) |journal=Nature Physics |volume=4 |issue=2 |year=2008 |pages=116–119 |doi=10.1038/nphys810 |bibcode=2008NatPh...4..116S |arxiv=0803.0744 |display-authors=etal}}</ref>) is thought to occur. It may therefore be a suitable material for constructing [[quantum computer]]s<ref>{{cite journal |arxiv=1003.4590 |title=Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force |first=Agung |last=Trisetyarso |journal=Quantum Information & Computation |url=http://dl.acm.org/citation.cfm?id=2481569.2481576 |volume=12 |year=2012 |page=989 |bibcode=2010arXiv1003.4590T |issue=11–12}}</ref> using [[anyon]]ic circuits.<ref>{{cite journal |arxiv=0812.1116 |title=Manifestations of topological effects in graphene |first=Jiannis K. |last=Pachos |journal=Contemporary Physics |doi=10.1080/00107510802650507 |volume=50 |year=2009 |pages=375–389 |bibcode=2009ConPh..50..375P |issue=2}}<br />{{cite web |url=http://www.int.washington.edu/talks/WorkShops/int_08_37W/People/Franz_M/Franz.pdf |title=Fractionalization of charge and statistics in graphene and related structures |first=M. |last=Franz |publisher=University of British Columbia |date=5 January 2008}}</ref>

====Half-integer quantum Hall effect====
[[File:Graphene - Geim - Landau levels.svg|thumb|290x290px|Landau levels in graphene appear at energies proportional to √N, in contrast to the standard sequence that goes as N+½.<ref name=geim2007/>]]
The [[quantum Hall effect]] is a quantum mechanical version of the [[Hall effect]], which is the production of transverse (perpendicular to the main current) conductivity in the presence of a [[magnetic field]]. The quantization of the [[Hall effect]] <math>\sigma_{xy}</math> at integer multiples (the "[[Landau level]]") of the basic quantity <math>e^2/h</math> (where ''e'' is the elementary electric charge and ''h'' is [[Planck's constant]]). It can usually be observed only in very clean [[silicon]] or [[gallium arsenide]] solids at temperatures around {{val|3 |ul=K}} and very high magnetic fields.

Graphene shows the quantum Hall effect with respect to conductivity quantization: the effect is ''anomalous'' in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy}=\pm {4\cdot\left(N + 1/2 \right)e^2}/h </math>, where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4.<ref name=geim2007/> These anomalies are present at room temperature, i.e. at roughly {{convert|20|C|K}}.<ref name=novo2005/>

This behavior is a direct result of graphene's massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the [[Atiyah–Singer index theorem]] and is half-filled in neutral graphene,<ref name="Semenoff" /> leading to the "+1/2" in the Hall conductivity.<ref name=gusy2005/> [[Bilayer graphene]] also shows the quantum Hall effect, but with only one of the two anomalies (i.e. <math>\sigma_{xy}=\pm {4\cdot N\cdot e^2}/h </math>). In the second anomaly, the first plateau at ''N=0'' is absent, indicating that bilayer graphene stays metallic at the neutrality point.<ref name=geim2007/>
[[File:Graphene - Geim - Chiral half-integer quantum Hall effect.svg|thumb|220x220px|Chiral half-integer quantum Hall effect in graphene. Plateaux in transverse conductivity appear at half integers of 4e²/h.<ref name=geim2007/>]]
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the [[Shubnikov–de Haas effect|Shubnikov–de Haas oscillations]], whereby the term ''integral'' quantum Hall effect. These oscillations show a phase shift of π, known as [[Geometric phase|Berry's phase]].<ref name=novo2005/><ref name="E-Phonon" /> Berry's phase arises due to the zero effective carrier mass near the Dirac points.<ref name=zhang2005/> The temperature dependence of the oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass.<ref name=novo2005/>

Graphene samples prepared on nickel films, and on both the silicon face and carbon face of [[silicon carbide#Structure and properties|silicon carbide]], show the anomalous effect directly in electrical measurements.<ref name="ByungHeeHong">{{cite journal |last1=Kim |first1=Kuen Soo |title=Large-scale pattern growth of graphene films for stretchable transparent electrodes |year=2009 |doi=10.1038/nature07719 |journal=Nature |volume=457 |pmid=19145232 |issue=7230 |bibcode=2009Natur.457..706K |pages=706–10 |last2=Zhao |first2=Yue |last3=Jang |first3=Houk |last4=Lee |first4=Sang Yoon |last5=Kim |first5=Jong Min |last6=Kim |first6=Kwang S. |last7=Ahn |first7=Jong-Hyun |last8=Kim |first8=Philip |last9=Choi |first9=Jae-Young |last10=Hong |first10=Byung Hee}}</ref><ref name="0908.1900" /><ref name="ShenAPL" /><ref name="0909.2903" /><ref name="0909.1193" /><ref name="phase1" /> Graphitic layers on the carbon face of silicon carbide show a clear [[Dirac spectrum]] in [[ARPES|angle-resolved photoemission]] experiments, and the effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{cite journal |first=Michael S. |last=Fuhrer |title=A physicist peels back the layers of excitement about graphene |doi=10.1038/4591037e |journal=Nature |volume=459 |page=1037 |year=2009 |pmid=19553953 |issue=7250 |bibcode=2009Natur.459.1037F}}</ref>

====Strong magnetic fields====

In magnetic fields above 10 [[Tesla (unit)|tesla]] or so additional plateaus of the Hall conductivity at {{nowrap |1=''σ''<sub>''xy''</sub> = ''νe''<sup>2</sup>/''h''}} with {{nowrap |1=''ν'' = 0, ±1, ±4}} are observed.<ref name="nu-0-1-4">{{cite journal |last1=Zhang |first1=Y. |last2=Jiang |first2=Z. |last3=Small |first3=J. P. |last4=Purewal |first4=M. S. |last5=Tan |first5=Y.-W. |last6=Fazlollahi |first6=M. |last7=Chudow |first7=J. D. |last8=Jaszczak |first8=J. A. |last9=Stormer |first9=H. L. |last10=Kim |first10=P. |title=Landau-Level Splitting in Graphene in High Magnetic Fields |doi=10.1103/PhysRevLett.96.136806 |pmid=16712020 |journal=Physical Review Letters |volume=96 |page=136806 |year=2006 |bibcode=2006PhRvL..96m6806Z |issue=13 |arxiv=cond-mat/0602649}}</ref> A plateau at {{nowrap |1=''ν'' = 3}}<ref name="nu-3">{{cite journal |last1=Du |first1=X. |last2=Skachko |first2=Ivan |last3=Duerr |first3=Fabian |last4=Luican |first4=Adina |last5=Andrei |first5=Eva Y. |title=Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene |doi=10.1038/nature08522 |journal=Nature |volume=462 |pages=192–195 |year=2009 |issue=7270 |pmid=19829294 |arxiv=0910.2532 |bibcode=2009Natur.462..192D}}</ref> and the [[fractional quantum Hall effect]] at {{nowrap |1=''ν'' = {{frac|1|3}}}} were also reported.<ref name="nu-3" /><ref name="nu-one3rd">{{cite journal |last1=Bolotin |first1=K. |last2=Ghahari |first2=Fereshte |last3=Shulman |first3=Michael D. |last4=Stormer |first4=Horst L. |last5=Kim |first5=Philip |title=Observation of the fractional quantum Hall effect in graphene |doi=10.1038/nature08582 |journal=Nature |volume=462 |pages=196–199 |year=2009 |issue=7270 |pmid=19881489 |arxiv=0910.2763 |bibcode=2009Natur.462..196B}}</ref>

These observations with {{nowrap |1=''ν'' = 0, ±1, ±3, ±4}} indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted.

====Casimir effect====

The [[Casimir effect]] is an interaction between disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the interacting bodies' surfaces. Since graphene/electromagnetic field interaction is strong for a one-atom-thick material, the Casimir effect is of growing interest.<ref name="BFGV">{{cite journal |last1=Bordag |first1=M. |last2=Fialkovsky |first2=I. V. |last3=Gitman |first3=D. M. |last4=Vassilevich |first4=D. V. |title=Casimir interaction between a perfect conductor and graphene described by the Dirac model |journal=Physical Review B |volume=80 |year=2009 |page=245406 |doi=10.1103/PhysRevB.80.245406 |bibcode=2009PhRvB..80x5406B |issue=24 |arxiv=0907.3242}}</ref><ref name="FMD">{{cite journal |last1=Fialkovsky |first1=I. V. |last2=Marachevsky |first2=V.N. |last3=Vassilevich |first3=D. V. |title=Finite temperature Casimir effect for graphene |year=2011 |volume=84 |issue=35446 |journal=Physical Review B |arxiv=1102.1757 |bibcode=2011PhRvB..84c5446F |page=35446 |doi=10.1103/PhysRevB.84.035446}}</ref>

====Van der Waals force====

The [[Van der Waals force]] (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic [[power law]] in contrast to the usual inverse quartic.<ref name="DWR">{{cite journal |last1=Dobson |first1=J. F. |last2=White |first2=A. |last3=Rubio |first3=A. |title=Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals |journal=Physical Review Letters |volume=96 |year=2006 |page=073201 |doi=10.1103/PhysRevLett.96.073201 |pmid=16606085 |issue=7 |bibcode=2006PhRvL..96g3201D |arxiv=cond-mat/0502422}}</ref>

===='Massive' electrons====

Graphene's unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing [[Boron nitride|hexagonal boron nitride]] (h-BN) in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV [0.03 Electron Volt(eV)].<ref name="sci1306">{{cite journal |last1=Fuhrer |first1=M. S. |title=Critical Mass in Graphene |doi=10.1126/science.1240317 |journal=Science |volume=340 |issue=6139 |pages=1413–1414 |year=2013 |pmid=23788788 |pmc= |bibcode=2013Sci...340.1413F}}</ref>

The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via [[optical spectroscopy]]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.<ref name="sci1306" />

If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of [[quantum dot]]s, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against [[backscatter]]ing and could carry currents without dissipation.<ref name="sci1306" />

===Permittivity===
Graphene's [[permittivity]] varies with frequency. Over a range from microwave to millimeter wave frequencies it is roughly 3.3.<ref name="cismaru">{{cite document |last1=Cismaru |first1=Alina |last2=Dragoman |first2=Mircea |last3=Dinescu |first3=Adrian |last4=Dragoman |first4=Daniela |last5=Stavrinidis |first5=G. |last6=Konstantinidis |first6=G. |title=Microwave and Millimeterwave Electrical Permittivity of Graphene Monolayer |arxiv=1309.0990 |year=2013 |bibcode=2013arXiv1309.0990C }}</ref> This permittivity, combined with the ability to form both conductors and insulators, means that theoretically, compact [[capacitor]]s made of graphene could store large amounts of electrical energy.

===Optical===

Graphene's unique optical properties produce an unexpectedly high [[Opacity (optics)|opacity]] for an atomic monolayer in vacuum, absorbing {{nowrap|''πα'' ≈ 2.3%}} of [[light]], from visible to infrared.<ref name=nair2008/><ref name=zhu2014/><ref>{{cite journal|last1=Kuzmenko|first1=A. B.|last2=Van Heumen|first2=E.|last3=Carbone|first3=F.|last4=Van Der Marel|first4=D.|year=2008|title=Universal infrared conductance of graphite|journal=Physical Review Letters|volume=100|issue=11|page=117401|arxiv=0712.0835|bibcode=2008PhRvL.100k7401K|doi=10.1103/PhysRevLett.100.117401|pmid=18517825}}</ref> Here, ''α'' is the [[fine-structure constant]]. This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole [[conical intersection|conical bands]] meeting each other at the [[graphene#Electronic properties|Dirac point]]... [which] is qualitatively different from more common [[quadratic massive band]]s."<ref name=nair2008/> Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, the interatomic distance, hopping value and frequency cancel when optical conductance is calculated using [[Fresnel equations]] in the thin-film limit.

Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the [[fine-structure constant]].<ref>{{cite web |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |website=ScienceDaily |date=4 April 2008}}</ref>

[[Multi-Parametric Surface Plasmon Resonance]] was used to characterize both thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. The measured refractive index and extinction coefficient values at {{convert|670|nm|m|abbr=on|lk=on}} wavelength are 3.135 and 0.897, respectively. The thickness was determined as 3.7Å from a 0.5mm area, which agrees with 3.35Å reported for layer-to-layer carbon atom distance of graphite crystals.<ref>{{cite journal |last1=Jussila |first1=Henri |last2=Yang |first2=He |last3=Granqvist |first3=Niko |last4=Sun |first4=Zhipei |title=Surface plasmon resonance for characterization of large-area atomic-layer graphene film |journal=Optica |date=5 February 2016 |volume=3 |issue=2 |pages=151–158 |doi=10.1364/OPTICA.3.000151|bibcode=2016Optic...3..151J }}</ref> The method can be further used also for real-time label-free interactions of graphene with organic and inorganic substances. Furthermore, the existence of unidirectional surface plasmons in the nonreciprocal graphene-based gyrotropic interfaces has been demonstrated theoretically. By efficiently controlling the chemical potential of graphene, the unidirectional working frequency can be continuously tunable from THz to near-infrared and even visible.<ref>{{cite journal|last1=Lin|first1=Xiao|last2=Xu|first2=Yang |last3=Zhang|first3=Baile|last4=Hao|first4=Ran|last5=Chen|first5=Hongsheng| last6=Li|first6=Erping|title=Unidirectional surface plasmons in nonreciprocal graphene|journal=New Journal of Physics|volume=15|issue=11|pages=113003|date=2013|doi=10.1088/1367-2630/15/11/113003|bibcode=2013NJPh...15k3003L|doi-access=free}}</ref> Particularly, the unidirectional frequency bandwidth can be 1– 2 orders of magnitude larger than that in metal under the same magnetic field, which arises from the superiority of extremely small effective electron mass in graphene.

Graphene's [[band gap]] can be tuned from 0 to {{val|0.25 |u=eV}} (about 5 micrometre wavelength) by applying voltage to a dual-gate [[bilayer graphene]] [[field-effect transistor]] (FET) at room temperature.<ref>{{cite journal |doi=10.1038/nature08105 |journal=Nature |last1=Zhang |first1=Y. |last2=Tang |first2=Tsung-Ta |last3=Girit |first3=Caglar |last4=Hao |first4=Zhao |last5=Martin |first5=Michael C. |last6=Zettl |first6=Alex |last7=Crommie |first7=Michael F. |last8=Shen |first8=Y. Ron |last9=Wang |first9=Feng |volume=459 |pages=820–823 |date=11 June 2009 |title=Direct observation of a widely tunable bandgap in bilayer graphene |pmid=19516337 |issue=7248 |bibcode=2009Natur.459..820Z|osti=974550 |url=https://www.osti.gov/biblio/974550 }}</ref> The optical response of [[graphene nanoribbons]] is tunable into the [[Terahertz radiation|terahertz]] regime by an applied magnetic field.<ref>{{cite journal |doi=10.1063/1.2964093 |journal=Appl Phys Lett |first1=Junfeng |last1=Liu |first2=A. R. |last2=Wright |first3=Chao |last3=Zhang |first4=Zhongshui |last4=Ma |volume=93 |pages=041106–041110 |date=29 July 2008 |title=Strong terahertz conductance of graphene nanoribbons under a magnetic field |bibcode=2008ApPhL..93d1106L |issue=4|url=https://ro.uow.edu.au/engpapers/3322 }}</ref> Graphene/graphene oxide systems exhibit [[Graphene#Electrochromic devices|electrochromic behavior]], allowing tuning of both linear and ultrafast optical properties.<ref name=kurum2011/>

A graphene-based [[Bragg grating]] (one-dimensional [[photonic crystal]]) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using {{convert|633|nm|m|abbr=on|lk=on}} He–Ne laser as the light source.<ref>{{cite journal |first1=K.V. |last2=Zeng |first2=Shuwen |last3=Shang |first3=Jingzhi |last4=Yong |first4=Ken-Tye |last5=Yu |first5=Ting |last1=Sreekanth |title=Excitation of surface electromagnetic waves in a graphene-based Bragg grating |journal=Scientific Reports |year=2012 |doi=10.1038/srep00737 |pmid=23071901 |volume=2 |page=737 |bibcode=2012NatSR...2E.737S |pmc=3471096}}</ref>

====Saturable absorption====

Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed [[saturable absorption]] and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to [[near-infrared]] region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of [[fiber laser]]s, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast [[photonics]]. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically.<ref name=kurum2011/><ref name=bao2009/><ref name=zhang2009a/><ref name=zhang2009b/><ref name=zhang2010a/><ref name=zhang2009c/>

Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave saturable absorption in graphene demonstrates the possibility of graphene microwave and terahertz photonics devices, such as a microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.<ref name=zheng2012/>

====Nonlinear Kerr effect====

Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to the optical nonlinear [[Kerr effect]]. Based on a typical open and close aperture z-scan measurement, graphene possesses a giant nonlinear Kerr coefficient of {{val |e=-7 |u=cm<sup>2</sup>⋅W<sup>−1</sup>}}, almost nine orders of magnitude larger than that of bulk dielectrics.<ref name="ZHANGHAN">{{cite journal |last1=Zhang |first1=H. |last2=Virally |first2=Stéphane |last3=Bao |first3=Qiaoliang |last4=Kian Ping |first4=Loh |last5=Massar |first5=Serge |last6=Godbout |first6=Nicolas |last7=Kockaert |first7=Pascal |title=Z-scan measurement of the nonlinear refractive index of graphene |journal=Optics Letters |year=2012 |volume=37 |issue=11 |pages=1856–1858 |doi=10.1364/OL.37.001856 |pmid=22660052 |bibcode=2012OptL...37.1856Z|arxiv=1203.5527 }}</ref> This suggests that graphene may be a powerful nonlinear Kerr medium, with the possibility of observing a variety of nonlinear effects, the most important of which is the [[soliton]].<ref>{{cite journal |last1=Dong |first1=H |last2=Conti |first2=C |last3=Marini |first3=A |last4=Biancalana |first4=F |year=2013 |title=Terahertz relativistic spatial solitons in doped graphene metamaterials |url= |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |volume=46 |issue= 15|page=15540|doi=10.1088/0953-4075/46/15/155401 |bibcode=2013JPhB...46o5401D |arxiv=1107.5803 }}</ref>

===Excitonic===

First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |pages=601–659 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last1=Onida |first1=Giovanni |last2=Rubio |first2=Angel |issue=2|hdl=10261/98472 |url=https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf }}</ref> With GW calculation, the properties of graphene-based materials are accurately investigated, including bulk graphene,<ref>{{cite journal |journal=Physical Review Letters |year=2009 |volume=103 |page=186802 |doi=10.1103/PhysRevLett.103.186802 |bibcode=2009PhRvL.103r6802Y |title=Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene |last1=Yang |first1=Li |last2=Deslippe |first2=Jack |last3=Park |first3=Cheol-Hwan |last4=Cohen |first4=Marvin |last5=Louie |first5=Steven |issue=18 |pmid=19905823 |arxiv=0906.0969}}</ref> [[graphene nanoribbons|nanoribbons]],<ref>{{cite journal |journal=Physical Review B |year=2008 |volume=77 |page=041404 |doi=10.1103/PhysRevB.77.041404 |title=Optical properties of graphene nanoribbons: The role of many-body effects |last1=Prezzi |first1=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |issue=4 |arxiv=0706.0916 |bibcode=2008PhRvB..77d1404P}}<br />{{cite journal |journal=Nano Letters |year=2007 |volume=7 |pages=3112–5 |doi=10.1021/nl0716404 |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=10 |pmid=17824720 |arxiv=0707.2983 |bibcode=2007NanoL...7.3112Y}}<br />{{cite journal |journal=Physical Review Letters |year=2008 |volume=101 |page=186401 |doi=10.1103/PhysRevLett.101.186401 |bibcode=2008PhRvL.101r6401Y |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=18 |pmid=18999843}}</ref> edge and surface functionalized armchair oribbons,<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |pages=17257–17262 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |issue=41|url=https://figshare.com/articles/Excitons_of_Edge_and_Surface_Functionalized_Graphene_Nanoribbons/2719792 }}</ref> hydrogen saturated armchair ribbons,<ref>{{cite journal |journal=Nanoscale |year=2011 |volume=3 |pages=2324–8 |doi=10.1039/c1nr10095e |title=Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons |last1=Wang |first1=Min |last2=Li |first2=Chang Ming |s2cid=31835103 |issue=5 |pmid=21503364 |bibcode=2011Nanos...3.2324W}}</ref> [[Josephson effect]] in graphene SNS junctions with single localized defect<ref>{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Josephson effect in graphene SNS junction with a single localized defect |journal=Physica B |volume=405 |pages=2896–2899 |year=2010 |doi=10.1016/j.physb.2010.04.015 |issue=13 |arxiv=1006.1391 |bibcode=2010PhyB..405.2896B}}<br />{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Tunneling conductance of the graphene SNS junction with a single localized defect |journal=Journal of Experimental and Theoretical Physics (JETP) |volume=110 |pages=613–617 |year=2010 |doi=10.1134/S1063776110040084 |issue=4 |arxiv=1006.1386 |bibcode=2010JETP..110..613B}}</ref> and armchair ribbon scaling properties.<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |pmid=21939213 |last1=Zhu |first1=Xi |last2=Su |first2=Haibin|bibcode=2011JPCA..11511998Z |url=https://figshare.com/articles/Scaling_of_Excitons_in_Graphene_Nanoribbons_with_Armchair_Shaped_Edges/2590648 }}</ref>

===Spin transport===

Graphene is claimed to be an ideal material for [[spintronics]] due to its small [[spin-orbit interaction]] and the near absence of [[nuclear magnetic moment]]s in carbon (as well as a weak [[hyperfine interaction]]). Electrical [[spin current]] injection and detection has been demonstrated up to room temperature.<ref name="Tombros">{{cite journal |title=Electronic spin transport and spin precession in single graphene layers at room temperature |bibcode=2007Natur.448..571T |last=Tombros |first=Nikolaos |journal=Nature |year=2007 |volume=448 |issue=7153 |pages=571–575 |doi=10.1038/nature06037 |pmid=17632544 |arxiv=0706.1948 |display-authors=etal}}</ref><ref name="ChoSpin">{{cite journal |first1=Sungjae |last1=Cho |first2=Yung-Fu |last2=Chen |first3=Michael S. |last3=Fuhrer |year=2007 |volume=91 |page=123105 |title=Gate-tunable Graphene Spin Valve |journal=Applied Physics Letters |doi=10.1063/1.2784934 |bibcode=2007ApPhL..91l3105C |issue=12 |arxiv=0706.1597}}</ref><ref name="Ohishi">{{cite journal |last=Ohishi |first=Megumi |year=2007 |volume=46 |issue=25 |pages=L605–L607 |title=Spin Injection into a Graphene Thin Film at Room Temperature |journal=Jpn J Appl Phys |doi=10.1143/JJAP.46.L605 |bibcode=2007JaJAP..46L.605O |arxiv=0706.1451 |display-authors=etal}}</ref> Spin coherence length above 1 micrometre at room temperature was observed,<ref name="Tombros" /> and control of the spin current polarity with an electrical gate was observed at low temperature.<ref name="ChoSpin" />

===Magnetic properties===

====Strong magnetic fields====

Graphene's quantum Hall effect in magnetic fields above 10 [[Tesla (unit)|Tesla]]s or so reveals additional interesting features. Additional plateaus of the Hall conductivity at <math>\sigma_{xy}=\nu e^2/h</math> with <math>\nu=0,\pm {1},\pm {4}</math> are observed.<ref name="nu-0-1-4" /> Also, the observation of a plateau at <math>\nu=3</math><ref name="nu-3" /> and the fractional quantum Hall effect at <math>\nu=1/3</math> were reported.<ref name="nu-3" /><ref name="nu-one3rd" />

These observations with <math>\nu=0,\pm 1,\pm 3, \pm 4</math> indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the [[magnetic catalysis]] of [[symmetry breaking]] is responsible for lifting the degeneracy.{{citation needed|date=December 2013}}

Spintronic and magnetic properties can be present in graphene simultaneously.<ref>{{cite journal |last1=Hashimoto |first1=T. |last2=Kamikawa |first2=S. |last3=Yagi |first3=Y. |last4=Haruyama |first4=J. |last5=Yang |first5=H. |last6=Chshiev |first6=M. |title=Graphene edge spins: spintronics and magnetism in graphene nanomeshes |journal=Nanosystems: Physics, Chemistry, Mathematics |date=2014 |volume=5 |issue=1 |pages=25–38 |url=http://nanojournal.ifmo.ru/en/wp-content/uploads/2014/02/NPCM51_P25-38.pdf}}</ref> Low-defect graphene nanomeshes manufactured by using a non-lithographic method exhibit large-amplitude ferromagnetism even at room temperature. Additionally a spin pumping effect is found for fields applied in parallel with the planes of few-layer ferromagnetic nanomeshes, while a magnetoresistance hysteresis loop is observed under perpendicular fields.

===Magnetic===
In 2014 researchers magnetized graphene by placing it on an atomically smooth layer of magnetic [[yttrium iron garnet]]. The graphene's electronic properties were unaffected. Prior approaches involved doping graphene with other substances.<ref>T. Hashimoto, S. Kamikawa, Y. Yagi, J. Haruyama, H. Yang, M. Chshiev, [http://nanojournal.ifmo.ru/en/articles-2/volume5/5-1/paper02/ "Graphene edge spins: spintronics and magnetism in graphene nanomeshes"], February 2014, Volume 5, Issue 1, pp 25</ref> The dopant's presence negatively affected its electronic properties.<ref>{{cite news |url=http://www.gizmag.com/magnetized-graphene/35805 |title=Scientists give graphene one more quality – magnetism |first=Ben |last=Coxworth |date=January 27, 2015 |accessdate=6 October 2016 |publisher=Gizmag}}</ref>

===Thermal conductivity===

Thermal transport in graphene is an active area of research, which has attracted attention because of the potential for thermal management applications. Following predictions for graphene and related [[carbon nanotubes]],<ref name="DT130">{{cite journal |last1=Berber |first1=Savas |last2=Kwon |first2=Young-Kyun |last3=Tománek |first3=David |title=Unusually High Thermal Conductivity of Carbon Nanotubes |journal=Phys. Rev. Lett. |date=2000 |volume=84 |issue=20 |pages=4613–6 |doi=10.1103/PhysRevLett.84.4613|pmid=10990753 |arxiv=cond-mat/0002414 |bibcode=2000PhRvL..84.4613B }}</ref> early measurements of the [[thermal conductivity]] of suspended graphene reported an exceptionally large thermal conductivity up to {{val|5300 |u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}},<ref name="Balandin">{{cite journal |last1=Balandin |first1=A. A. |last2=Ghosh |first2=Suchismita |last3=Bao |first3=Wenzhong |last4=Calizo |first4=Irene |last5=Teweldebrhan |first5=Desalegne |last6=Miao |first6=Feng |last7=Lau |first7=Chun Ning |s2cid=9310741 |date=20 February 2008 |doi=10.1021/nl0731872 |title=Superior Thermal Conductivity of Single-Layer Graphene |journal=  Nano Letters|pmid=18284217 |volume=8 |issue=3 |pages=902–907 |bibcode=2008NanoL...8..902B}}</ref> compared with the thermal conductivity of pyrolytic [[graphite]] of approximately {{val|2000 |u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} at room temperature.<ref name="Touloukian1970">{{cite book |author=Y S. Touloukian |title=Thermophysical Properties of Matter: Thermal conductivity : nonmetallic solids |url={{google books |plainurl=y |id=31sqAAAAYAAJ}} |year=1970 |publisher=IFI/Plenum |isbn=978-0-306-67020-6}}</ref> However, later studies primarily on more scalable but more defected graphene derived by Chemical Vapor Deposition have been unable to reproduce such high thermal conductivity measurements, producing a wide range of thermal conductivities between {{val|1500}} – {{val|2500 |u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} for suspended single layer graphene .<ref name="CaiMoore2010">{{cite journal |last1=Cai |first1=Weiwei |last2=Moore |first2=Arden L. |last3=Zhu |first3=Yanwu |last4=Li |first4=Xuesong |last5=Chen |first5=Shanshan |last6=Shi |first6=Li |last7=Ruoff |first7=Rodney S. |s2cid=207664146 |title=Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition |journal=Nano Letters |volume=10 |issue=5 |year=2010 |pages=1645–1651 |issn=1530-6984 |doi=10.1021/nl9041966 |pmid=20405895 |bibcode=2010NanoL..10.1645C}}</ref><ref name="FaugerasFaugeras2010">{{cite journal |last1=Faugeras |first1=Clement |last2=Faugeras |first2=Blaise |last3=Orlita |first3=Milan |last4=Potemski |first4=M. |last5=Nair |first5=Rahul R. |last6=Geim |first6=A. K. |title=Thermal Conductivity of Graphene in Corbino Membrane Geometry |journal=ACS Nano |volume=4 |issue=4 |year=2010 |pages=1889–1892 |issn=1936-0851 |doi=10.1021/nn9016229|pmid=20218666 |arxiv=1003.3579 |bibcode=2010arXiv1003.3579F }}</ref><ref name="XuPereira2014">{{cite journal |last1=Xu |first1=Xiangfan |last2=Pereira |first2=Luiz F. C. |last3=Wang |first3=Yu |last4=Wu |first4=Jing |last5=Zhang |first5=Kaiwen |last6=Zhao |first6=Xiangming |last7=Bae |first7=Sukang |last8=Tinh Bui |first8=Cong |last9=Xie |first9=Rongguo |last10=Thong |first10=John T. L. |last11=Hong |first11=Byung Hee |last12=Loh |first12=Kian Ping |last13=Donadio |first13=Davide |last14=Li |first14=Baowen |last15=Özyilmaz |first15=Barbaros |title=Length-dependent thermal conductivity in suspended single-layer graphene |journal=Nature Communications |volume=5 |pages=3689 |year=2014 |issn=2041-1723 |doi=10.1038/ncomms4689 |pmid=24736666 |arxiv=1404.5379 |bibcode=2014NatCo...5.3689X}}</ref><ref name="LeeYoon2011">{{cite journal |last1=Lee |first1=Jae-Ung |last2=Yoon |first2=Duhee |last3=Kim |first3=Hakseong |last4=Lee |first4=Sang Wook |last5=Cheong |first5=Hyeonsik |title=Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy |journal=Physical Review B |volume=83 |issue=8 |pages=081419 |year=2011 |issn=1098-0121 |doi=10.1103/PhysRevB.83.081419 |arxiv=1103.3337 |bibcode=2011PhRvB..83h1419L}}</ref> The large range in the reported thermal conductivity can be caused by large measurement uncertainties as well as variations in the graphene quality and processing conditions.
In addition, it is known that when single-layer graphene is supported on an amorphous material, the thermal conductivity is reduced to about {{val|500}} – {{val|600 |u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} at room temperature as a result of scattering of graphene lattice waves by the substrate,<ref name="SeolJo2010">{{cite journal |last1=Seol |first1=J. H. |last2=Jo |first2=I. |last3=Moore |first3=A. L. |last4=Lindsay |first4=L. |last5=Aitken |first5=Z. H. |last6=Pettes |first6=M. T. |last7=Li |first7=X. |last8=Yao |first8=Z. |last9=Huang |first9=R. |last10=Broido |first10=D. |last11=Mingo |first11=N. |last12=Ruoff |first12=R. S. |last13=Shi |first13=L. |s2cid=213783 |title=Two-Dimensional Phonon Transport in Supported Graphene |journal=Science |volume=328 |issue=5975 |year=2010 |pages=213–216 |issn=0036-8075 |doi=10.1126/science.1184014 |pmid=20378814 |bibcode=2010Sci...328..213S}}</ref><ref name="Klemens2001">{{cite journal |last1=Klemens |first1=P. G. |title=Theory of Thermal Conduction in Thin Ceramic Films |journal=International Journal of Thermophysics |volume=22 |issue=1 |year=2001 |pages=265–275 |issn=0195-928X |doi=10.1023/A:1006776107140}}</ref> and can be even lower for few layer graphene encased in amorphous oxide.<ref name="JangChen2010">{{cite journal |last1=Jang |first1=Wanyoung |last2=Chen |first2=Zhen |last3=Bao |first3=Wenzhong |last4=Lau |first4=Chun Ning |last5=Dames |first5=Chris |s2cid=45253497 |title=Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite |journal=Nano Letters |volume=10 |issue=10 |year=2010 |pages=3909–3913 |issn=1530-6984 |doi=10.1021/nl101613u |pmid=20836537 |bibcode=2010NanoL..10.3909J}}</ref> Likewise, polymeric residue can contribute to a similar decrease in the thermal conductivity of suspended graphene to approximately {{val|500}} – {{val|600 |u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}}for bilayer graphene.<ref name="PettesJo2011">{{cite journal |last1=Pettes |first1=Michael Thompson |last2=Jo |first2=Insun |last3=Yao |first3=Zhen |last4=Shi |first4=Li |title=Influence of Polymeric Residue on the Thermal Conductivity of Suspended Bilayer Graphene |journal=Nano Letters |volume=11 |issue=3 |year=2011 |pages=1195–1200 |issn=1530-6984 |doi=10.1021/nl104156y |pmid=21314164 |bibcode=2011NanoL..11.1195P}}</ref>

It has been suggested that the isotopic composition, the ratio of [[Carbon-12|<sup>12</sup>C]] to [[Carbon-13|<sup>13</sup>C]], has a significant impact on the thermal conductivity. For example, isotopically pure <sup>12</sup>C graphene has higher thermal conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name="chen2012natmat">{{cite journal |first1=Shanshan |last1=Chen |first2=Qingzhi |last2=Wu |first3=Columbia |last3=Mishra |first4=Junyong |last4=Kang |first5=Hengji |last5=Zhang |first6=Kyeongjae |last6=Cho |first7=Weiwei |last7=Cai |first8=Alexander A. |last8=Balandin |first9=Rodney S. |last9=Ruoff |publication-date=10 January 2012 |title=Thermal conductivity of isotopically modified graphene |journal=[[Nature Materials]] |volume=11 |issue=3 |pages=203–207 |doi=10.1038/nmat3207 |pmid=22231598 |year=2012 |arxiv=1112.5752 |bibcode=2012NatMa..11..203C}}<br />''Lay summary'': {{cite news |publication-date=12 January 2012 |title=Keeping Electronics Cool |periodical=[[Scientific Computing (periodical)|Scientific Computing]] |at=scientificcomputing.com |publisher=[[Advantage Business Media]] |url=http://www.scientificcomputing.com/news-HPC-Keeping-Electronics-Cool-011212.aspx?et_cid=2422972&et_rid=220285420&linkid=http%3a%2f%2fwww.scientificcomputing.com%2fnews-HPC-Keeping-Electronics-Cool-011212.aspx |first=Suzanne |last=Tracy |date=12 January 2012}}</ref> It can be shown by using the [[Wiedemann–Franz law]], that the thermal conduction is [[phonon]]-dominated.<ref name="Balandin" /> However, for a gated graphene strip, an applied gate bias causing a [[Fermi energy]] shift much larger than ''k''<sub>B</sub>''T'' can cause the electronic contribution to increase and dominate over the [[phonon]] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito">{{cite journal |journal=[[Physical Review B]] |last1=Saito |first1=K. |last2=Nakamura |first2=J. |last3=Natori |first3=A. |title=Ballistic thermal conductance of a graphene sheet |volume=76 |page=115409 |year=2007 |doi=10.1103/PhysRevB.76.115409 |bibcode=2007PhRvB..76k5409S |issue=11}}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |first1=Qizhen |last1=Liang |first2=Xuxia |last2=Yao |first3=Wei |last3=Wang |first4=Yan |last4=Liu |first5=Ching Ping |last5=Wong |year=2011 |title=A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |journal=ACS Nano |pmid=21384860 |volume=5 |issue=3 |pages=2392–2401 |doi=10.1021/nn200181e|url=https://figshare.com/articles/A_Three_Dimensional_Vertically_Aligned_Functionalized_Multilayer_Graphene_Architecture_An_Approach_for_Graphene_Based_Thermal_Interfacial_Materials/2680561 }}</ref>

Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has [[basal plane]] [[thermal conductivity]] of over a {{val|1000 |u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} (comparable to [[diamond]]). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger [[lattice spacing]].<ref>{{cite book |url={{google books |plainurl=y |id=7p2pgNOWPbEC}} |title=Graphite and Precursors |last=Delhaes |first=P. |publisher=CRC Press |year=2001 |isbn=978-90-5699-228-6}}</ref> In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.<ref name="mingo">{{cite journal |last1=Mingo |first1=N. |last2=Broido |first2=D.A. |title=Carbon Nanotube Ballistic Thermal Conductance and Its Limits |doi=10.1103/PhysRevLett.95.096105 |pmid=16197233 |journal=Physical Review Letters |volume=95 |page=096105 |year=2005 |bibcode=2005PhRvL..95i6105M |issue=9}}</ref>

Despite its 2-D nature, graphene has 3 [[acoustic phonon]] modes. The two in-plane modes (LA, TA) have a linear [[dispersion relation]], whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the ''T''<sup>2</sup> dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T<sup>1.5</sup> contribution of the out of plane mode.<ref name="mingo" /> Some graphene phonon bands display negative [[Grüneisen parameter]]s.<ref name="mounet">{{cite journal |last1=Mounet |first1=N. |last2=Marzari |first2=N. |title=First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives |doi=10.1103/PhysRevB.71.205214 |journal=Physical Review B |volume=71 |page=205214 |year=2005 |arxiv=cond-mat/0412643 |bibcode=2005PhRvB..71t5214M |issue=20}}</ref> At low temperatures (where most optical modes with positive Grüneisen parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant and [[thermal expansion coefficient]] (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transverse acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane [[lattice parameter]] since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string, which, when it is stretched, will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect," was predicted by [[Ilya Mikhailovich Lifshitz|Lifshitz]] in 1952.<ref name="lifshitz">{{cite journal|last=Lifshitz|first=I.M.|year=1952|title=|url=|journal=Journal of Experimental and Theoretical Physics|language=ru|volume=22|page=475|via=}}</ref>

===Mechanical===
The (two-dimensional) density of graphene is 0.763&nbsp;mg per square meter.{{cn|date=July 2020}}

Graphene is the strongest material ever tested,<ref name=lee2008/><ref name=cao2020/> with an intrinsic [[tensile strength]] of {{convert|130|GPa|abbr=on|lk=on}} (with representative engineering tensile strength ~50-60 GPa for stretching large-area freestanding graphene) and a [[Young's modulus]] (stiffness) close to {{convert|1|TPa|abbr=on|lk=on}}. The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a {{val|4 |u=kg}} cat but would weigh only as much as one of the cat's whiskers, at {{val|0.77 |u=mg}} (about 0.001% of the weight of {{val|1 |u=m<sup>2</sup>}} of paper).<ref name="nobelprize.org">{{cite web |url=https://selectra.co.uk/sites/selectra.co.uk/files/pdf/advanced-physicsprize2010.pdf |title=2010 Nobel Physics Laureates |publisher=nobelprize.org}}</ref>

Large-angle-bent graphene monolayer has been achieved with negligible strain, showing mechanical robustness of the two-dimensional carbon nanostructure. Even with extreme deformation, excellent carrier mobility in monolayer graphene can be preserved.<ref>{{cite journal|last1=Briggs|first1=Benjamin D.|last2=Nagabhirava|first2=Bhaskar|last3=Rao|first3=Gayathri|last4=Deer|first4=Robert|last5=Gao|first5=Haiyuan|last6=Xu|first6=Yang|last7=Yu|first7=Bin|title=Electromechanical robustness of monolayer graphene with extreme bending|journal=Applied Physics Letters |volume=97|issue=22|pages=223102|date=2010|doi=10.1063/1.3519982|bibcode=2010ApPhL..97v3102B}}</ref>

The [[spring constant]] of suspended graphene sheets has been measured using an [[atomic force microscope]] (AFM). Graphene sheets were suspended over {{chem|SiO|2}} cavities where an AFM tip was used to apply a stress to the sheet to test its mechanical properties. Its spring constant was in the range 1–5&nbsp;N/m and the stiffness was {{val|0.5 |u=TPa}}, which differs from that of bulk graphite. These intrinsic properties could lead to applications such as [[Nanoelectromechanical systems|NEMS]] as pressure sensors and resonators.<ref>{{cite journal |last1=Frank |first1=I. W. |last2=Tanenbaum |first2=D. M. |last3=Van Der Zande |first3=A.M. |last4=McEuen |first4=P. L. |title=Mechanical properties of suspended graphene sheets |doi=10.1116/1.2789446 |journal=J. Vac. Sci. Technol. B |volume=25 |pages=2558–2561 |year=2007 |url=http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |bibcode=2007JVSTB..25.2558F |issue=6}}</ref> Due to its large surface energy and out of plane ductility, flat graphene sheets are unstable with respect to scrolling, i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name="nmscrolling">{{cite journal |first1=S. |last1=Braga |first2=V. R. |last2=Coluci |first3=S. B. |last3=Legoas |first4=R. |last4=Giro |first5=D. S. |last5=Galvão |first6=R. H. |last6=Baughman |year=2004 |title=Structure and Dynamics of Carbon Nanoscrolls |journal=Nano Letters |volume=4 |pages=881–884 |doi=10.1021/nl0497272 |bibcode=2004NanoL...4..881B |issue=5}}</ref>

As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the [[Mermin–Wagner theorem]] shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name=meyer2007/> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.<ref name=geim2007/><ref name=carl2007/><ref name=faso2007/><ref name=bolm2011a/><ref name=bolm2011b/> It has recently been shown that these ripples, if amplified through the introduction of vacancy defects, can impart a negative [[Poisson's ratio]] into graphene, resulting in the thinnest [[auxetic]] material known so far.<ref name=grima2014/>

Graphene nanosheets have been incorporated into a Ni matrix through a plating process to form Ni-graphene composites on a target substrate. The enhancement in mechanical properties of the composites is attributed to the high interaction between Ni and graphene and the prevention of the dislocation sliding in the Ni matrix by the graphene.<ref>{{cite journal|last1= Ren|first1=Zhaodi|last2=Meng|first2=Nan|last3=Shehzad|first3=Khurram|last4=Xu|first4=Yang|last5=Qu|first5=Shaoxing|last6=Yu|first6=Bin|last7=Luo|first7=Jack|title=Mechanical properties of nickel-graphene composites synthesized by electrochemical deposition|journal=Nanotechnology
|volume=26|issue=6|pages=065706|date=2015|doi=10.1088/0957-4484/26/6/065706|pmid=25605375|bibcode=2015Nanot..26f5706R|url=http://ubir.bolton.ac.uk/1575/1/Mechanical%20properties%20of%20nickel-graphene%20composites%20synthesized%20by%20electrochemical%20deposition.pdf}}</ref>

====Fracture toughness====
In 2014, researchers from [[Rice University]] and the [[Georgia Institute of Technology]] have indicated that despite its strength, graphene is also relatively brittle, with a fracture toughness of about 4 MPa√m.<ref name="ZhangMa2014">{{cite journal |last1=Zhang |first1=Peng |last2=Ma |first2=Lulu |last3=Fan |first3=Feifei |last4=Zeng |first4=Zhi |last5=Peng |first5=Cheng |last6=Loya |first6=Phillip E. |last7=Liu |first7=Zheng |last8=Gong |first8=Yongji |last9=Zhang |first9=Jiangnan |last10=Zhang |first10=Xingxiang |last11=Ajayan |first11=Pulickel M. |last12=Zhu |first12=Ting |last13=Lou |first13=Jun |title=Fracture toughness of graphene |journal=Nature Communications |volume=5 |pages=3782 |year=2014 |issn=2041-1723 |doi=10.1038/ncomms4782 |pmid=24777167 |bibcode=2014NatCo...5.3782Z|doi-access=free }}</ref> This indicates that imperfect graphene is likely to crack in a brittle manner like [[ceramic materials]], as opposed to many metallic materials which tend to have fracture toughnesses in the range of 15–50&nbsp;MPa√m. Later in 2014, the Rice team announced that graphene showed a greater ability to distribute force from an impact than any known material, ten times that of steel per unit weight.<ref>{{Cite news |url=http://singularityhub.com/2014/12/04/graphene-armor-would-be-light-flexible-and-far-stronger-than-steel/ |title=Graphene Armor Would Be Light, Flexible and Far Stronger Than Steel |last=Dorrieron |first=Jason |date=4 December 2014 |work=Singularity Hub |accessdate=6 October 2016}}</ref> The force was transmitted at {{convert|22.2|km/s}}.<ref>{{cite news |url=http://www.gizmag.com/graphene-bulletproof-armor/35004 |title=Graphene could find use in lightweight ballistic body armor |first=Ben |last=Coxworth |date=1 December 2014 |work=Gizmag |accessdate=6 October 2016}}</ref>

====Mechanical properties of polycrystalline graphene====
Various methods – most notably, [[chemical vapor deposition]] (CVD), as discussed in the section below - have been developed to produce large-scale graphene needed for device applications. Such methods often synthesize polycrystalline graphene.<ref name=":5">{{Cite journal|last1=Papageorgiou|first1=Dimitrios G.|last2=Kinloch|first2=Ian A.|last3=Young|first3=Robert J.|date=2017-10-01|title=Mechanical properties of graphene and graphene-based nanocomposites|journal=Progress in Materials Science|volume=90|pages=75–127|doi=10.1016/j.pmatsci.2017.07.004|issn=0079-6425|doi-access=free}}</ref> The mechanical properties of polycrystalline graphene is affected by the nature of the defects, such as [[Grain boundary|grain-boundaries (GB)]] and [[Vacancy defect|vacancies]], present in the system and the average grain-size. How the mechanical properties change with such defects have been investigated by researchers, theoretically and experimentally.<ref name=":6">{{Cite journal|last1=Zhu|first1=Yong|last2=Zhou|first2=Yao|last3=Zhang|first3=Yong Wei|last4=Zhang|first4=Teng|last5=Yakobson|first5=Boris I.|last6=Wang|first6=Peng|last7=Reed|first7=Evan J.|last8=Park|first8=Harold S.|last9=Lu|first9=Nanshu|date=2017-05-01|title=A review on mechanics and mechanical properties of 2D materials—Graphene and beyond|url=https://experts.syr.edu/en/publications/a-review-on-mechanics-and-mechanical-properties-of-2d-materialsgr|journal=Extreme Mechanics Letters|volume=13|pages=42–77|doi=10.1016/j.eml.2017.01.008|issn=2352-4316|arxiv=1611.01555}}</ref><ref name=":5" /><ref name=":7">{{Cite journal|last1=Zhang|first1=Teng|last2=Li|first2=Xiaoyan|last3=Gao|first3=Huajian|date=2015-11-01|title=Fracture of graphene: a review|journal=International Journal of Fracture|volume=196|issue=1|pages=1–31|doi=10.1007/s10704-015-0039-9|issn=1573-2673}}</ref><ref name=":8">{{Cite journal|last1=Isacsson|first1=Andreas|last2=Cummings|first2=Aron W|last3=Colombo|first3=Luciano|last4=Colombo|first4=Luigi|last5=Kinaret|first5=Jari M|last6=Roche|first6=Stephan|date=2016-12-19|title=Scaling properties of polycrystalline graphene: a review|journal=2D Materials|volume=4|issue=1|pages=012002|doi=10.1088/2053-1583/aa5147|issn=2053-1583|arxiv=1612.01727}}</ref>

Graphene grain boundaries typically contain heptagon-pentagon pairs. The arrangement of such defects depends on whether the GB is in zig-zag or armchair direction. It further depends on the tilt-angle of the GB.<ref>{{Cite journal|last=Li|first=J. C. M.|date=1972-06-01|title=Disclination model of high angle grain boundaries|journal=Surface Science|volume=31|pages=12–26|doi=10.1016/0039-6028(72)90251-8|issn=0039-6028|bibcode=1972SurSc..31...12L}}</ref> In 2010, researchers from Brown University computationally predicted that as the tilt-angle increases, the grain boundary strength also increases.They showed that the weakest link in the grain boundary is at the critical bonds of the heptagon rings. As the grain boundary angle increases, the strain in these heptagon rings decreases, causing the grain-boundary to be stronger than lower-angle GBs. They proposed that, in fact, for sufficiently large angle GB, the strength of the GB is similar to pristine graphene.<ref>{{Cite journal|last1=Grantab|first1=Rassin|last2=Shenoy|first2=Vivek B.|last3=Ruoff|first3=Rodney S.|date=2010-11-12|title=Anomalous strength characteristics of tilt grain boundaries in graphene|journal=Science|volume=330|issue=6006|pages=946–948|doi=10.1126/science.1196893|issn=1095-9203|pmid=21071664|bibcode=2010Sci...330..946G|arxiv=1007.4985}}</ref> In 2012, it was further shown that the strength can increase or decrease, depending on the detailed arrangements of the defects.<ref>{{Cite journal|last1=Wei|first1=Yujie|last2=Wu|first2=Jiangtao|last3=Yin|first3=Hanqing|last4=Shi|first4=Xinghua|last5=Yang|first5=Ronggui|last6=Dresselhaus|first6=Mildred|date=September 2012|title=The nature of strength enhancement and weakening by pentagon-heptagon defects in graphene|journal=Nature Materials|volume=11|issue=9|pages=759–763|doi=10.1038/nmat3370|issn=1476-1122|pmid=22751178|bibcode=2012NatMa..11..759W|url=http://dspace.imech.ac.cn/handle/311007/46051}}</ref> These predictions have since been supported by experimental evidences. In a 2013 study led by James Hone's group, researchers probed the elastic [[stiffness]] and [[Strength of materials|strength]] of CVD-grown graphene by combining nano-indentation and high-resolution [[Transmission electron microscopy|TEM]]. They found that the elastic stiffness is identical and strength is only slightly lower than those in pristine graphene.<ref>{{Cite journal|last1=Lee|first1=Gwan-Hyoung|last2=Cooper|first2=Ryan C.|last3=An|first3=Sung Joo|last4=Lee|first4=Sunwoo|last5=van der Zande|first5=Arend|last6=Petrone|first6=Nicholas|last7=Hammerberg|first7=Alexandra G.|last8=Lee|first8=Changgu|last9=Crawford|first9=Bryan|date=2013-05-31|title=High-strength chemical-vapor-deposited graphene and grain boundaries|journal=Science|volume=340|issue=6136|pages=1073–1076|doi=10.1126/science.1235126|issn=1095-9203|pmid=23723231|bibcode=2013Sci...340.1073L}}</ref> In the same year, researchers from UC Berkeley and UCLA probed bi-crystalline graphene with [[Transmission electron microscopy|TEM]] and [[Atomic force microscopy|AFM]]. They found that the strength of grain-boundaries indeed tend to increase with the tilt angle.<ref>{{Cite journal|last1=Gimzewski|first1=James K.|last2=Zettl|first2=A.|last3=Klug|first3=William S.|last4=Ophus|first4=Colin|last5=Rasool|first5=Haider I.|date=2013-11-19|title=Measurement of the intrinsic strength of crystalline and polycrystalline graphene|journal=Nature Communications|volume=4|pages=2811|doi=10.1038/ncomms3811|issn=2041-1723|bibcode=2013NatCo...4.2811R|doi-access=free}}</ref>

While the presence of vacancies is not only prevalent in polycrystalline graphene, vacancies can have significant effects on the strength of graphene. The general consensus is that the strength decreases along with increasing densities of vacancies. In fact, various studies have shown that for graphene with sufficiently low density of vacancies, the strength does not vary significantly from that of pristine graphene. On the other hand, high density of vacancies can severely reduce the strength of graphene.<ref name=":7" />

Compared to the fairly well-understood nature of the effect that grain boundary and vacancies have on the mechanical properties of graphene, there is no clear consensus on the general effect that the average grain size has on the strength of polycrystalline graphene.<ref name=":6" /><ref name=":7" /><ref name=":8" /> In fact, three notable theoretical/computational studies on this topic have led to three different conclusions.<ref name=":9">{{Cite journal|last1=Kotakoski|first1=Jani|last2=Meyer|first2=Jannik C.|date=2012-05-24|title=Mechanical properties of polycrystalline graphene based on a realistic atomistic model|journal=Physical Review B|volume=85|issue=19|pages=195447|doi=10.1103/PhysRevB.85.195447|bibcode=2012PhRvB..85s5447K|arxiv=1203.4196}}</ref><ref name=":10">{{Cite journal|last1=Song|first1=Zhigong|last2=Artyukhov|first2=Vasilii I.|last3=Yakobson|first3=Boris I.|last4=Xu|first4=Zhiping|s2cid=17221784|date=2013-04-10|title=Pseudo Hall–Petch Strength Reduction in Polycrystalline Graphene|journal=Nano Letters|volume=13|issue=4|pages=1829–1833|doi=10.1021/nl400542n|pmid=23528068|issn=1530-6984|bibcode=2013NanoL..13.1829S}}</ref><ref name=":11">{{Cite journal|last1=Sha|first1=Z. D.|last2=Quek|first2=S. S.|last3=Pei|first3=Q. X.|last4=Liu|first4=Z. S.|last5=Wang|first5=T. J.|last6=Shenoy|first6=V. B.|last7=Zhang|first7=Y. W.|date=2014-08-08|title=Inverse Pseudo Hall-Petch Relation in Polycrystalline Graphene|journal=Scientific Reports|volume=4|pages=5991|doi=10.1038/srep05991|issn=2045-2322|pmc=4125985|pmid=25103818|bibcode=2014NatSR...4E5991S}}</ref> First, in 2012, Kotakoski and Myer studied the mechanical properties of polycrystalline graphene with "realistic atomistic model", using [[Molecular dynamics|molecular-dynamics]] (MD) simulation. To emulate the growth mechanism of CVD, they first randomly selected [[nucleation]] sites that are at least 5A (arbitrarily chosen) apart from other sites. Polycrystalline graphene was generated from these nucleation sites and was subsequently annealed at 3000K, then quenched. Based on this model, they found that cracks are initiated at grain-boundary junctions, but the grain size does not significantly affect the strength.<ref name=":9" /> Second, in 2013, Z. Song et al. used MD simulations to study the mechanical properties of polycrystalline graphene with uniform-sized hexagon-shaped grains. The hexagon grains were oriented in various lattice directions and the GBs consisted of only heptagon, pentagon, and hexagonal carbon rings. The motivation behind such model was that similar systems had been experimentally observed in graphene flakes grown on the surface of liquid copper. While they also noted that crack is typically initiated at the triple junctions, they found that as the grain size decreases, the yield strength of graphene increases. Based on this finding, they proposed that polycrystalline follows pseudo [[Hall-Petch relationship]].<ref name=":10" /> Third, in 2013, Z. D. Sha et al. studied the effect of grain size on the properties of polycrystalline graphene, by modelling the grain patches using [[Voronoi diagram|Voronoi construction]]. The GBs in this model consisted of heptagon, pentagon, and hexagon, as well as squares, octagons, and vacancies. Through MD simulation, contrary to the fore-mentioned study, they found inverse Hall-Petch relationship, where the strength of graphene increases as the grain size increases.<ref name=":11" /> Experimental observations and other theoretical predictions also gave differing conclusions, similar to the three given above.<ref name=":8" /> Such discrepancies show the complexity of the effects that grain size, arrangements of defects, and the nature of defects have on the mechanical properties of polycrystalline graphene.

===Biological===
Researchers at the Graphene Research Centre at the National University of Singapore (NUS) discovered in 2011 the ability of graphene to accelerate the [[osteogenic]] differentiation of human [[Mesenchymal stem cell|Mesenchymal Stem Cells]] without the use of biochemical inducers.<ref>{{Cite journal|last1=Nayak|first1=Tapas R.|last2=Andersen|first2=Henrik|last3=Makam|first3=Venkata S.|last4=Khaw|first4=Clement|last5=Bae|first5=Sukang|last6=Xu|first6=Xiangfan|last7=Ee|first7=Pui-Lai R.|last8=Ahn|first8=Jong-Hyun|last9=Hong|first9=Byung Hee|date=2011-06-28|title=Graphene for Controlled and Accelerated Osteogenic Differentiation of Human Mesenchymal Stem Cells|journal=ACS Nano|volume=5|issue=6|pages=4670–4678|doi=10.1021/nn200500h|pmid=21528849|issn=1936-0851|bibcode=2011arXiv1104.5120N|arxiv=1104.5120}}</ref>

In 2015 researchers used graphene to create sensitive biosensors by using epitaxial graphene on silicon carbide. The sensors bind to the 8-hydroxydeoxyguanosine (8-OHdG) and is capable of selective binding with [[antibodies]]. The presence of 8-OHdG in blood, urine and saliva is commonly associated with DNA damage. Elevated levels of 8-OHdG have been linked to increased risk of developing several cancers.<ref>{{Cite journal |title=Generic epitaxial graphene biosensors for ultrasensitive detection of cancer risk biomarker |last=Tehrani |first=Z. |date=2014-09-01 |journal=2D Materials |doi=10.1088/2053-1583/1/2/025004 |pmid= |bibcode=2014TDM.....1b5004T |volume=1 |issue=2 |page=025004|url=https://cronfa.swan.ac.uk/Record/cronfa19735/Download/0019735-07052015130054.pdf }}</ref>

The Cambridge Graphene Centre and the University of Trieste in Italy conducted a collaborative research on use of Graphene as electrodes to interact with brain neurons. The research was recently published in the journal of ACS Nano.

The research revealed that uncoated Graphene can be used as neuro-interface electrode without altering or damaging the neural functions such as signal loss or formation of scar tissue. Graphene electrodes in body stay significantly more stable than modern day electrodes (of tungsten or silicon) because of its unique properties such as flexibility, bio-compatibility, and conductivity. It could possibly help in restoring sensory function or motor disorders in paralysis or Parkinson patients.<ref>{{cite web |title=Graphene shown to safely interact with neurons in the brain |url=https://www.cam.ac.uk/research/news/graphene-shown-to-safely-interact-with-neurons-in-the-brain |website=University of Cambridge |date=2016-01-29 |access-date=2016-02-16}}</ref>

===Support substrate===
The electronics property of graphene can be significantly influenced by the supporting substrate. Studies of graphene monolayers on clean and hydrogen(H)-passivated silicon (100) (Si(100)/H) surfaces have been performed.<ref>{{cite journal|last1=Xu|first1=Yang|last2=He|first2=K. T.|last3=Schmucker|first3=S. W.|last4=Guo|first4=Z.|last5=Koepke|first5=J. C.|last6=Wood|first6=J. D.|last7=Lyding|first7=J. W.|last8=Aluru|first8=N. R.|s2cid=207573621|title=Inducing Electronic Changes in Graphene through Silicon (100) Substrate Modification|journal=Nano Letters|volume=11|issue=7|pages=2735–2742|date=2011|doi=10.1021/nl201022t|pmid=21661740|bibcode=2011NanoL..11.2735X}}</ref> The Si(100)/H surface does not perturb the electronic properties of graphene, whereas the interaction between the clean Si(100) surface and graphene changes the electronic states of graphene significantly. This effect results from the covalent bonding between C and surface Si atoms, modifying the π-orbital network of the graphene layer. The local density of states shows that the bonded C and Si surface states are highly disturbed near the Fermi energy.

==Forms==

===Monolayer sheets===
In 2013 a group of Polish scientists presented a production unit that allows the manufacture of continuous monolayer sheets.<ref>{{cite journal |title=Single and Multilayer Growth of Graphene from the Liquid Phase |journal=Applied Mechanics and Materials |volume=510 |pages=8–12 |doi=10.4028/www.scientific.net/AMM.510.8 |year=2014 |last1=Kula |first1=Piotr |last2=Pietrasik |first2=Robert |last3=Dybowski |first3=Konrad |last4=Atraszkiewicz |first4=Radomir |last5=Szymanski |first5=Witold |last6=Kolodziejczyk |first6=Lukasz |last7=Niedzielski |first7=Piotr |last8=Nowak |first8=Dorota }}</ref> The process is based on graphene growth on a liquid metal matrix.<ref>{{cite web |title=Polish scientists find way to make super-strong graphene sheets {{!}} Graphene-Info |url=http://www.graphene-info.com/polish-scientists-find-way-make-super-strong-graphene-sheets |website=www.graphene-info.com |accessdate=2015-07-01}}</ref> The product of this process was called [[HSMG]].

===Bilayer graphene===
{{main|Bilayer graphene}}

Bilayer graphene displays the [[anomalous quantum Hall effect]], a tunable [[band gap]]<ref name="PRB75.155115">{{cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 |last1=Min |first1=Hongki |last2=Sahu |first2=Bhagawan |last3=Banerjee |first3=Sanjay |last4=MacDonald |first4=A. |journal=Physical Review B |volume=75 |issue=15 |page=155115 |arxiv=cond-mat/0612236 |bibcode=2007PhRvB..75o5115M}}</ref> and potential for [[Exciton#Interaction|excitonic condensation]]<ref name="PRL104.096802">{{cite journal |doi=10.1103/PhysRevLett.104.096802 |pmid=20367001 |title=Anomalous Exciton Condensation in Graphene Bilayers |year=2010 |last1=Barlas |first1=Yafis |last2=Côté |first2=R. |last3=Lambert |first3=J. |last4=MacDonald |first4=A. H. |journal=Physical Review Letters |volume=104 |issue=9 |page=96802 |bibcode=2010PhRvL.104i6802B |arxiv=0909.1502}}</ref>&nbsp;–making it a promising candidate for [[optoelectronic]] and [[nanoelectronic]] applications. Bilayer graphene typically can be found either in [[Twistronics|twisted]] configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other.<ref name="nl204547v">{{cite journal |doi=10.1021/nl204547v |pmid=22329410 |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 |last1=Min |first1=Lola |last2=Hovden |first2=Robert |last3=Huang |journal=Nano Letters |volume=12 |issue=3 |first3=Pinshane |last4=Wojcik |first4=Michal |last5=Muller |first5=David A. |last6=Park |first6=Jiwoong |s2cid=896422 |pages=1609–1615 |bibcode=2012NanoL..12.1609B}}</ref> Stacking order and orientation govern the optical and electronic properties of bilayer graphene.

One way to synthesize bilayer graphene is via [[chemical vapor deposition]], which can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v" /> In 2014, researchers at [[University of California, Santa Barbara]] and [[Rice University]], reported a rapid synthesis technique for [[Wafer (electronics)|wafer-scale]] (> 3 [[Inch|in.]] square) and high-quality AB or [[Bilayer graphene|bernal-stacked]] bilayer CVD graphene.<ref>{{Cite journal|last1=Liu|first1=Wei|last2=Krämer|first2=Stephan|last3=Sarkar|first3=Deblina|last4=Li|first4=Hong|last5=Ajayan|first5=Pulickel M.|last6=Banerjee|first6=Kaustav|date=December 5, 2013|title=Controllable and rapid synthesis of high-quality and large-area bernal stacked bilayer graphene using chemical vapor deposition|journal=Chemistry of Materials|volume=26|issue=2|pages=907–915|doi=10.1021/cm4021854}}</ref><ref>{{Cite news|last=|first=|url=https://www.sciencedaily.com/releases/2014/05/140501101125.htm|title=New rapid synthesis developed for bilayer graphene and high-performance transistors|date=May 1, 2014|work=ScienceDaily|access-date=|url-status=live}}</ref>

It has been shown that the two graphene layers can withstand important strain or doping mistmach<ref>{{cite journal |last1=Forestier |first1=Alexis |last2=Balima |first2=Félix |last3=Bousige |first3=Colin |last4=de Sousa Pinheiro |first4=Gardênia |last5=Fulcrand |first5=Rémy |last6=Kalbác |first6=Martin |last7=San-Miguel |first7=Alfonso |title=Strain and Piezo-Doping Mismatch between Graphene Layers |journal=J. Phys. Chem. C |date=April 28, 2020 |volume=124 |issue=20 |page=11193|doi=10.1021/acs.jpcc.0c01898 |url=https://pubs.acs.org/doi/abs/10.1021/acs.jpcc.0c01898}}</ref> which ultimately should lead to their exfoliation.

===Graphene superlattices===

Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities in designing nanoelectronic and photonic devices. Various types of superlattices can be obtained by stacking graphene and its related forms.<ref>{{cite journal|last1=Xu|first1=Yang|last2=Liu|first2=Yunlong|last3=Chen|first3=Huabin|last4=Lin|first4=Xiao|last5=Lin|first5=Shisheng|last6=Yu|first6=Bin|last7=Luo|first7=Jikui|title=Ab initio study of energy-band modulation ingraphene-based two-dimensional layered superlattices|journal=Journal of Materials Chemistry|volume=22|issue=45|pages=23821|date=2012|doi=10.1039/C2JM35652J}}</ref> The energy band in layer-stacked superlattices is found to be more sensitive to the barrier width than that in conventional III–V semiconductor superlattices. When adding more than one atomic layer to the barrier in each period, the coupling of electronic wavefunctions in neighboring potential wells can be significantly reduced, which leads to the degeneration of continuous subbands into quantized energy levels. When varying the well width, the energy levels in the potential wells along the L-M direction behave distinctly from those along the K-H direction.

===Graphene nanoribbons===

[[File:Graphene edge names.svg|thumb|upright=1.2|Names for graphene edge topologies]]
[[File:Cnt zz v3.gif|thumb|upright=1.5|[[Graphene nanoribbon|GNR]] Electronic band structure of graphene strips of varying widths in zig-zag orientation. Tight-binding calculations show that they are all metallic.]]

[[File:Cnt gnrarm v3.gif|thumb|upright=1.5|[[Graphene nanoribbon|GNR]] Electronic band structure of grahene strips of various widths in the armchair orientation. Tight-binding calculations show that they are semiconducting or metallic depending on width (chirality).]]

[[Graphene nanoribbons]] ("nanostripes" in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of [[spintronics]]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{cite journal |first1=A Castro |last1=Neto |last2=Peres |first2=N. M. R. |last3=Novoselov |first3=K. S. |last4=Geim |first4=A. K. |last5=Geim |first5=A. K. |title=The electronic properties of graphene |journal=Rev Mod Phys |volume=81 |issue=1 |year=2009 |pages=109–162 |url=http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |archive-url=https://web.archive.org/web/20101115121052/http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |url-status=dead |archive-date=2010-11-15 |bibcode=2009RvMP...81..109C |doi=10.1103/RevModPhys.81.109 |arxiv=0709.1163|hdl=10261/18097 }}</ref>)

===Graphene quantum dots===
A [[graphene quantum dot]] (GQD) is a graphene fragment with size less than 100 nm.  The properties of GQDs are different from 'bulk' graphene due to the quantum confinement effects which is only become apparent when size is smaller than 100&nbsp;nm. <ref name=tang2014/><ref name=tang2012/><ref name=tang2013/>

===Graphene oxide===
{{further|Graphite oxide}}

Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called [[graphene oxide paper]], have a measured [[tensile modulus]] of 32 [[GPa]].<ref>{{cite web |url=http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archiveurl=https://web.archive.org/web/20160602213039/http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archivedate=2 June 2016 |title=Graphene Oxide Paper |publisher=Northwestern University |accessdate=28 February 2011}}</ref> The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes.<ref>{{cite journal |last1=Eftekhari |first1=Ali |last2=Yazdani |first2=Bahareh |title=Initiating electropolymerization on graphene sheets in graphite oxide structure |journal=Journal of Polymer Science Part A: Polymer Chemistry |volume=48 |pages=2204–2213 |year=2010 |doi=10.1002/pola.23990 |bibcode=2010JPoSA..48.2204E |issue=10}}</ref> Graphene oxide flakes in polymers display enhanced photo-conducting properties.<ref>{{cite journal |last1=Nalla |first1=Venkatram |last2=Polavarapu |first2=L |last3=Manga |first3=KK |last4=Goh |first4=BM |last5=Loh |first5=KP |last6=Xu |first6=QH |last7=Ji |first7=W |title=Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite |journal=Nanotechnology |volume=21 |issue=41 |page=415203 |year=2010 |pmid=20852355 |doi=10.1088/0957-4484/21/41/415203 |bibcode=2010Nanot..21O5203N}}</ref> Graphene is normally hydrophobic and impermeable to all gases and liquids (vacuum-tight). However, when formed into graphene oxide-based capillary membrane, both liquid water and water vapor flow through as quickly as if the membrane was not present.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 |last1=Nair |first1=R. R. |last2=Wu |first2=H. A. |last3=Jayaram |first3=P. N. |last4=Grigorieva |first4=I. V. |last5=Geim |first5=A. K. |bibcode=2012Sci...335..442N}}</ref>

===Chemical modification===

[[File:slgo.jpg|left|upright=1.3|thumb|Photograph of single-layer graphene oxide undergoing high temperature chemical treatment, resulting in sheet folding and loss of carboxylic functionality, or through room temperature carbodiimide treatment, collapsing into star-like clusters.]] Soluble fragments of graphene can be prepared in the laboratory<ref>{{cite journal |first1=Sandip |last1=Niyogi |first2=Elena |last2=Bekyarova |first3=Mikhail E. |last3=Itkis |first4=Jared L. |last4=McWilliams |first5=Mark A. |last5=Hamon |first6=Robert C. |last6=Haddon |title=Solution Properties of Graphite and Graphene |journal=[[J. Am. Chem. Soc.]] |volume=128 |pages=7720–7721 |year=2006 |doi=10.1021/ja060680r |pmid=16771469 |issue=24}}</ref> through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and [[nitric acid]]. A series of oxidation and exfoliation steps produce small graphene plates with [[carboxyl]] groups at their edges. These are converted to [[acid chloride]] groups by treatment with [[thionyl chloride]]; next, they are converted to the corresponding graphene [[amide]] via treatment with octadecylamine. The resulting material (circular graphene layers of {{convert|5.3|angstrom|m|abbr=on|lk=on|disp=or}} thickness) is soluble in [[tetrahydrofuran]], [[tetrachloromethane]] and [[1,2-Dichloroethane|dichloroethane]].

Refluxing single-layer graphene oxide (SLGO) in [[solvent]]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependent on their preparation methodology. When using thionyl chloride, [[acyl chloride]] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.

[[File:Graphene chemistry.jpg|upright=1.75|thumb|Boehm titration results for various chemical reactions of single-layer graphene oxide, which reveal reactivity of the carboxylic groups and the resultant stability of the SLGO sheets after treatment.]]

[[Hydrazine]] reflux is commonly used for reducing SLGO to SLG(R), but [[titration]]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with [[carbodiimide]]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (c. 3–5% conversion of the intermediate to the final amide).<ref>{{cite journal |first1=Raymond L.D. |last1=Whitby |first2=Alina |last2=Korobeinyk |first3=Katya V. |last3=Glevatska |title=Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry |journal=[[Carbon (journal)|Carbon]] |volume=49 |issue=2 |pages=722–725 |year=2011 |doi=10.1016/j.carbon.2010.09.049}}</ref> It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reactions types have been explored. SLGO has also been grafted with [[polyallylamine]], cross-linked through [[epoxy]] groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.<ref>{{cite journal |first1=Sungjin |last1=Park |first2=Dmitriy A. |last2=Dikin |first3=SonBinh T. |last3=Nguyen |first4=Rodney S. |last4=Ruoff |s2cid=55033112 |title=Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine |journal=[[J. Phys. Chem. C]] |volume=113 |pages=15801–15804 |year=2009 |doi=10.1021/jp907613s |issue=36}}</ref>

Full [[hydrogenation]] from both sides of graphene sheet results in [[graphane]], but partial hydrogenation leads to hydrogenated graphene.<ref>{{cite journal |first1=D. C. |last1=Elias |last2=Nair |first2=R. R. |last3=Mohiuddin |first3=T. M. G. |last4=Morozov |first4=S. V. |last5=Blake |first5=P. |last6=Halsall |first6=M. P. |last7=Ferrari |first7=A. C. |last8=Boukhvalov |first8=D. W. |last9=Katsnelson |first9=M. I. |last10=Geim |first10=A. K. |last11=Novoselov |first11=K. S. |title=Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane |journal=Science |year=2009 |volume=323 |doi=10.1126/science.1167130 |pmid=19179524 |issue=5914 |bibcode=2009Sci...323..610E |pages=610–3 |arxiv=0810.4706}}</ref> Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to [[fluorographene]] (graphene fluoride),<ref>{{cite journal |last1=Garcia |first1=J. C. |last2=de Lima |first2=D. B. |last3=Assali |first3=L. V. C. |last4=Justo |first4=J. F. |title=Group IV graphene- and graphane-like nanosheets |journal=J. Phys. Chem. C |date=2011 |volume=115 |issue=27 |pages=13242–13246 |doi=10.1021/jp203657w|arxiv=1204.2875 }}</ref> while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene.

===Graphene ligand/complex===

Graphene can be a [[ligand]] to coordinate metals and metal ions by introducing functional groups. Structures of graphene ligands are similar to e.g. metal-[[porphyrin]] complex, metal-[[phthalocyanine]] complex, and metal-[[phenanthroline]] complex. Copper and nickel ions can be coordinated with graphene ligands.<ref>{{cite journal |doi=10.1016/j.carbon.2011.03.056 |title=Exfoliated graphene ligands stabilizing copper cations |journal=Carbon |volume=49 |issue=10 |pages=3375–3378 |year=2011 |last1=Yamada |first1=Y. |last2=Miyauchi |first2=M. |last3=Kim |first3=J. |last4=Hirose-Takai |first4=K. |last5=Sato |first5=Y. |last6=Suenaga |first6=K. |last7=Ohba |first7=T. |last8=Sodesawa |first8=T. |last9=Sato |first9=S.}}<br/>{{cite journal |last1=Yamada |first1=Y. |last2=Miyauchi |first2=M. |last3=Jungpil |first3=K. |title=Exfoliated graphene ligands stabilizing copper cations |journal=Carbon |doi=10.1016/j.carbon.2011.03.056 |volume=49 |issue=10 |pages=3375–3378 |display-authors=etal|year=2011 }}</ref><ref>{{cite journal |doi=10.1016/j.carbon.2014.03.036 |title=Functionalized graphene sheets coordinating metal cations |journal=Carbon |volume=75 |pages=81–94 |year=2014 |last1=Yamada |first1=Y. |last2=Suzuki |first2=Y. |last3=Yasuda |first3=H. |last4=Uchizawa |first4=S. |last5=Hirose-Takai |first5=K. |last6=Sato |first6=Y. |last7=Suenaga |first7=K. |last8=Sato |first8=S.}}<br/>{{cite journal |title=Functionalized graphene sheets coordinating metal cations |last1=Yamada |first1=Y. |last2=Suzuki |first2=Y. |last3=Yasuda |first3=H. |journal=Carbon |doi=10.1016/j.carbon.2014.03.036 |volume=75 |pages=81–94 |display-authors=etal|year=2014 }}</ref>

===Graphene fiber===

In 2011, researchers reported a novel yet simple approach to fabricate graphene fibers from chemical vapor deposition grown graphene films.<ref>{{cite journal |doi=10.1021/la202380g |pmid=21875131 |title=Directly Drawing Self-Assembled, Porous, and Monolithic Graphene Fiber from Chemical Vapor Deposition Grown Graphene Film and Its Electrochemical Properties |journal=Langmuir |volume=27 |issue=19 |pages=12164–71 |date=29 August 2011 |last1=Li |first1=Xinming |last2=Zhao |first2=Tianshuo |last3=Wang |first3=Kunlin |last4=Yang |first4=Ying |last5=Wei |first5=Jinquan |last6=Kang |first6=Feiyu |last7=Wu |first7=Dehai |last8=Zhu |first8=Hongwei|url=https://figshare.com/articles/Directly_Drawing_Self_Assembled_Porous_and_Monolithic_Graphene_Fiber_from_Chemical_Vapor_Deposition_Grown_Graphene_Film_and_Its_Electrochemical_Properties/2608015 }}</ref> The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable surface tension. Flexible all-solid-state supercapacitors based on this graphene fibers were demonstrated in 2013.<ref>{{cite journal |title=Flexible all solid-state supercapacitors based on chemical vapor deposition derived graphene fibers |journal=Physical Chemistry Chemical Physics |volume=15 |issue=41 |pages=17752–7 |date=3 September 2013|doi=10.1039/C3CP52908H |pmid=24045695 |last1=Li |first1=Xinming |last2=Zhao |first2=Tianshuo |last3=Chen |first3=Qiao |last4=Li |first4=Peixu |last5=Wang |first5=Kunlin |last6=Zhong |first6=Minlin |last7=Wei |first7=Jinquan |last8=Wu |first8=Dehai |last9=Wei |first9=Bingqing |last10=Zhu |first10=Hongwei |s2cid=22426420 |bibcode=2013PCCP...1517752L }}</ref>

In 2015 intercalating small graphene fragments into the gaps formed by larger, coiled graphene sheets, after annealing provided pathways for conduction, while the fragments helped reinforce the fibers.{{fragment |date=May 2016}} The resulting fibers offered better thermal and electrical conductivity and mechanical strength. Thermal conductivity reached {{convert|1290|W/m/K|W/m/K|abbr=in|lk=on}}, while tensile strength reached {{convert|1080|MPa|abbr=on|lk=on}}.<ref>{{Cite journal |title=Highly thermally conductive and mechanically strong graphene fibers |first1=Guoqing |last1=Xin |first2=Tiankai |last2=Yao |first3=Hongtao |last3=Sun |first4=Spencer Michael |last4=Scott |first5=Dali |last5=Shao |first6=Gongkai |last6=Wang |first7=Jie |last7=Lian |date=September 4, 2015 |journal=Science |doi=10.1126/science.aaa6502 |pmid= 26339027|volume=349 |issue=6252 |pages=1083–1087 |bibcode=2015Sci...349.1083X|doi-access=free }}</ref>

In 2016, Kilometer-scale continuous graphene fibers with outstanding mechanical properties and excellent electrical conductivity are produced by high-throughput wet-spinning of graphene oxide liquid crystals followed by graphitization through a full-scale synergetic defect-engineering strategy.<ref>{{cite journal|last1= Xu|first1=Zhen|last2=Liu|first2=Yingjun|last3=Zhao|first3=Xiaoli|last4=Li|first4=Peng|last5=Sun|first5=Haiyan|last6=Xu|first6=Yang|last7=Ren|first7=Xibiao|last8=Jin|first8=Chuanhong|last9=Xu|first9=Peng|last10=Wang|first10=Miao|last11=Gao|first11=Chao|title=Ultrastiff and Strong Graphene Fibers via Full-Scale Synergetic Defect Engineering|journal= Advanced Materials|volume=28|issue=30|pages=6449–6456|date=2016|doi=10.1002/adma.201506426|pmid=27184960}}</ref> The graphene fibers with superior performances promise wide applications in functional textiles, lightweight motors, microelectronic devices, etc.

Tsinghua University in Beijing, led by Wei Fei of the Department of Chemical Engineering, claims to be able to create a carbon nanotube fibre which has a tensile strength of {{convert|80|GPa|abbr=on|lk=on}}.<ref>{{cite journal|last1=Bai|first1=Yunxiang|last2=Zhang|first2=Rufan|last3=Ye|first3=Xuan|last4=Zhu|first4=Zhenxing|last5=Xie|first5=Huanhuan|last6=Shen|first6=Boyuan|last7=Cai|first7=Dali|last8=Liu|first8=Bofei|last9=Zhang|first9=Chenxi|last10=Jia|first10=Zhao|last11=Zhang|first11=Shenli|last12=Li|first12=Xide|last13=Wei|first13=Fei|date=2018|title=Carbon nanotube bundles with tensile strength over 80 GPa.|journal=Nature Nanotechnology|volume=13|issue=7|pages=589–595|doi=10.1038/s41565-018-0141-z|pmid=29760522|bibcode=2018NatNa..13..589B}}</ref>

===3D graphene===

In 2013, a three-dimensional [[honeycomb]] of hexagonally arranged carbon was termed 3D graphene. Recently, self-supporting 3D graphene has also been produced.<ref>{{cite journal |last1=Wang |first1=H. |last2=Sun |first2=K. |last3=Tao |first3=F. |last4=Stacchiola |first4=D. J. |last5=Hu |first5=Y. H. |title=3D Honeycomb-Like Structured Graphene and Its High Efficiency as a Counter-Electrode Catalyst for Dye-Sensitized Solar Cells |doi=10.1002/ange.201303497 |journal=Angewandte Chemie |volume=125 |issue=35 |pages=9380–9384 |year=2013 |pmid= |pmc=}}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |accessdate=24 August 2013 |last1=Wang |first1=Hui |last2=Sun |first2=Kai |last3=Tao |first3=Franklin |last4=Stacchiola |first4=Dario J. |last5=Hu |first5=Yun Hang |journal=Angewandte Chemie |volume=125 |issue=35 |pages=9380–9384 |doi=10.1002/ange.201303497 |year=2013}}</ref> 3D structures of graphene can be fabricated by using either CVD or solution based methods. A recent review by Khurram and Xu et al., have provided the summary of the state-of-the-art techniques for fabrication of the 3D structure of graphene and other related two-dimensional materials.<ref name="auto">{{cite journal |last1=Shehzad |first1=Khurram |last2=Xu |first2=Yang |last3=Gao |first3=Chao |last4=Xianfeng |first4=Duan |title=Three-dimensional macro-structures of two-dimensional nanomaterials |journal=Chemical Society Reviews |volume=45 |issue=20 |pages=5541–5588 |date=2016 |doi=10.1039/C6CS00218H |pmid=27459895 }}</ref>
Recently, researchers at Stony Brook University have reported a novel radical-initiated crosslinking method to fabricate porous 3D free-standing architectures of graphene and carbon nanotubes using nanomaterials as building blocks without any polymer matrix as support.<ref name="PMID 23436939">{{cite journal |last1=Lalwani |first1=Gaurav |last2=Trinward Kwaczala |first2=Andrea |last3=Kanakia |first3=Shruti |last4=Patel |first4=Sunny C. |last5=Judex |first5=Stefan |last6=Sitharaman |first6=Balaji |year=2013 |title=Fabrication and characterization of three-dimensional macroscopic all-carbon scaffolds. |journal=Carbon |volume=53 |pages=90–100 |doi=10.1016/j.carbon.2012.10.035 |url=  |pmid=23436939 |pmc=3578711}}</ref> These 3D graphene (all-carbon) scaffolds/foams have applications in several fields such as energy storage, filtration, thermal management and biomedical devices and implants.<ref name="auto"/><ref name="PMID 25788440">{{cite journal |last1=Lalwani |first1=Gaurav |last2=Gopalan |first2=Anu Gopalan |last3=D'Agati |first3=Michael |last4=Srinivas Sankaran |first4=Jeyantt |last5=Judex |first5=Stefan |last6=Qin |first6=Yi-Xian |last7=Sitharaman |first7=Balaji |year=2015 |title=Porous three-dimensional carbon nanotube scaffolds for tissue engineering |journal=Journal of Biomedical Materials Research Part A |volume=103 |issue=10 |pages=3212–3225 |doi=10.1002/jbm.a.35449 |url=  |pmid=25788440|pmc=4552611 }}</ref>

Box-shaped graphene (BSG) [[nanostructure]] appeared after mechanical cleavage of [[pyrolytic graphite]] has been reported recently.<ref name="stm2016">{{cite journal |author=R. V. Lapshin |year=2016 |title=STM observation of a box-shaped graphene nanostructure appeared after mechanical cleavage of pyrolytic graphite |journal=Applied Surface Science |volume=360 |pages=451–460 |publisher=Elsevier B. V. |location=Netherlands |issn=0169-4332 |doi=10.1016/j.apsusc.2015.09.222 |url=http://www.niifp.ru/staff/lapshin/en/index.htm#stm2016 |format=PDF |bibcode=2016ApSS..360..451L |arxiv=1611.04379 |access-date=27 December 2015 |archive-url=https://web.archive.org/web/20081202033454/http://www.niifp.ru/staff/lapshin/en/index.htm#stm2016 |archive-date=2 December 2008 |url-status=dead }}</ref> The discovered nanostructure is a multilayer system of parallel hollow nanochannels located along the surface and having quadrangular cross-section. The thickness of the channel walls is approximately equal to 1&nbsp;nm. Potential fields of BSG application include: ultra-sensitive [[detector]]s, high-performance catalytic cells, nanochannels for [[DNA]] [[sequencing]] and manipulation, high-performance heat sinking surfaces, [[rechargeable battery|rechargeable batteries]] of enhanced performance, [[nanomechanical resonator]]s, electron multiplication channels in emission [[nanoelectronics|nanoelectronic]] devices, high-capacity [[sorbent]]s for safe [[hydrogen storage]].

Three dimensional bilayer graphene has also been reported.<ref>{{cite journal |author=Harris PJF |title=Hollow structures with bilayer graphene walls |journal=Carbon |volume=50 |issue=9 |pages=3195–3199 |year=2012 |doi=10.1016/j.carbon.2011.10.050
|url=https://zenodo.org/record/896080 }}</ref><ref>{{cite journal |vauthors=Harris PJ, Slater TJ, Haigh SJ, Hage FS, Kepaptsoglou DM, Ramasse QM, Brydson R |title=Bilayer graphene formed by passage of current through graphite: evidence for a three dimensional structure |journal=Nanotechnology |volume=25 |issue=46 |pages=465601 |year=2014 |doi=10.1088/0957-4484/25/46/465601 |pmid=25354780 |bibcode=2014Nanot..25.5601H|url=http://centaur.reading.ac.uk/38041/1/3D%20FOR%20NANOTECHNOLOGY%20SUBMITTED%20REVISED%20with%20figs.pdf }}</ref>

===Pillared graphene===
{{main|Pillared graphene}}
Pillared graphene is a hybrid carbon, structure consisting of an oriented array of carbon nanotubes connected at each end to a sheet of graphene. It was first described theoretically by George Froudakis and colleagues of the University of Crete in Greece in 2008. Pillared graphene has not yet been synthesised in the laboratory, but it has been suggested that it may have useful electronic properties, or as a hydrogen storage material.

===Reinforced graphene===

Graphene reinforced with embedded [[carbon nanotube]] reinforcing bars ("[[rebar]]") is easier to manipulate, while improving the electrical and mechanical qualities of both materials.<ref name="kurz5011">{{cite web|url=http://www.kurzweilai.net/carbon-nanotubes-as-reinforcing-bars-to-strengthen-graphene-and-increase-conductivity|title=Carbon nanotubes as reinforcing bars to strengthen graphene and increase conductivity|last=|first=|date=9 April 2014|website=|publisher=Kurzweil Library|url-status=live|archive-url=|archive-date=|accessdate=23 April 2014}}</ref><ref>{{cite journal |doi=10.1021/nn501132n |pmid=24694285 |pmc=4046778 |title=Rebar Graphene |journal=ACS Nano |year=2014 |last1=Yan |first1=Z. |last2=Peng |first2=Z. |last3=Casillas |first3=G. |last4=Lin |first4=J. |last5=Xiang |first5=C. |last6=Zhou |first6=H. |last7=Yang |first7=Y. |last8=Ruan |first8=G. |last9=Raji |first9=A. R. O. |last10=Samuel |first10=E. L. G. |last11=Hauge |first11=R. H. |last12=Yacaman |first12=M. J. |last13=Tour |first13=J. M. |volume=8|issue=5 |pages=5061–8 }}</ref>

Functionalized single- or multiwalled carbon nanotubes are spin-coated on copper foils and then heated and cooled, using the nanotubes themselves as the carbon source. Under heating, the functional [[carbon group]]s decompose into graphene, while the nanotubes partially split and form in-plane [[covalent bond]]s with the graphene, adding strength. [[Pi stacking|π–π stacking]] domains add more strength. The nanotubes can overlap, making the material a better conductor than standard CVD-grown graphene. The nanotubes effectively bridge the [[grain boundary|grain boundaries]] found in conventional graphene. The technique eliminates the traces of substrate on which later-separated sheets were deposited using epitaxy.<ref name=kurz5011/>

Stacks of a few layers have been proposed as a cost-effective and physically flexible replacement for [[indium tin oxide]] (ITO) used in displays and [[photovoltaic cell]]s.<ref name=kurz5011/>

===Molded graphene===
In 2015, researchers from the [[University of Illinois at Urbana–Champaign|University of Illinois at Urbana-Champaign]] (UIUC) developed a new approach for forming 3D shapes from flat, 2D sheets of graphene.<ref>{{Cite web|title=Robust new process forms 3D shapes from flat sheets of graphene|url=https://grainger.illinois.edu/news/11255|last=|first=|date=2015-06-23|website=grainger.illinois.edu|language=en|url-status=live|archive-url=|archive-date=|access-date=2020-05-31}}</ref> A film of graphene that had been soaked in solvent to make it swell and become malleable was overlaid on an underlying substrate "former". The solvent evaporated over time, leaving behind a layer of graphene that had taken on the shape of the underlying structure. In this way they were able to produce a range of relatively intricate micro-structured shapes.<ref>{{cite web|url=https://newatlas.com/3d-shapes-graphene-uiuc/38164/|title=Graphene takes on a new dimension|last=Jeffrey|first=Colin|date=June 28, 2015|website=New Atlas|url-status=live|archive-url=|archive-date=|accessdate=2019-11-10}}</ref> Features vary from 3.5 to 50 μm. Pure graphene and gold-decorated graphene were each successfully integrated with the substrate.<ref>{{cite web|url=http://www.kurzweilai.net/how-to-form-3-d-shapes-from-flat-sheets-of-graphene|title=How to form 3-D shapes from flat sheets of graphene|last=|first=|date=June 30, 2015|website=Kurzweil Library|url-status=live|archive-url=|archive-date=|accessdate=2019-11-10}}</ref>

===Graphene aerogel===
An [[aerogel]] made of graphene layers separated by carbon nanotubes was measured at 0.16 milligrams per cubic centimeter. A solution of graphene and carbon nanotubes in a mold is freeze dried to dehydrate the solution, leaving the aerogel. The material has superior elasticity and absorption. It can recover completely after more than 90% compression, and absorb up to 900 times its weight in oil, at a rate of 68.8 grams per second.<ref>{{cite web |title=Graphene aerogel is seven times lighter than air, can balance on a blade of grass - Slideshow {{!}} ExtremeTech |url=http://www.extremetech.com/extreme/153063-graphene-aerogel-is-seven-times-lighter-than-air-can-balance-on-a-blade-of-grass |website=ExtremeTech |accessdate=2015-10-11 |date=April 10, 2013 |first=Sebastian |last=Anthony}}</ref>

===Graphene nanocoil===
In 2015 a coiled form of graphene was discovered in graphitic carbon (coal). The spiraling effect is produced by defects in the material's hexagonal grid that causes it to spiral along its edge, mimicking a [[Riemann surface]], with the graphene surface approximately perpendicular to the axis. When voltage is applied to such a coil, current flows around the spiral, producing a magnetic field. The phenomenon applies to spirals with either zigzag or armchair patterns, although with different current distributions. Computer simulations indicated that a conventional spiral inductor of 205 microns in diameter could be matched by a nanocoil just 70 nanometers wide, with a field strength reaching as much as 1 [[Tesla (unit)|tesla]].<ref name=":0">{{cite web|url=http://www.kurzweilai.net/graphene-nano-coils-discovered-to-be-powerful-natural-electromagnets|title=Graphene nano-coils discovered to be powerful natural electromagnets|last=|first=|date=October 16, 2015|website=Kurzweil Library|url-status=live|archive-url=|archive-date=|accessdate=2019-11-10}}</ref>

The nano-solenoids analyzed through computer models at Rice should be capable of producing powerful magnetic fields of about 1&nbsp;tesla, about the same as the coils found in typical loudspeakers, according to Yakobson and his team – and about the same field strength as some MRI machines. They found the magnetic field would be strongest in the hollow, nanometer-wide cavity at the spiral's center.<ref name=":0" />

A [[solenoid]] made with such a coil behaves as a quantum conductor whose current distribution between the core and exterior varies with applied voltage, resulting in nonlinear [[inductance]].<ref>{{Cite journal |title=Riemann Surfaces of Carbon as Graphene Nanosolenoids |journal=Nano Letters |volume=16 |issue=1 |pages=34–9 |date=2015-10-14 |doi=10.1021/acs.nanolett.5b02430 |pmid=26452145 |first1=Fangbo |last1=Xu |first2=Henry |last2=Yu |first3=Arta |last3=Sadrzadeh |first4=Boris I. |last4=Yakobson |bibcode=2016NanoL..16...34X}}</ref>

===Crumpled graphene===


In 2016, [[Brown University]] introduced a method for 'crumpling' graphene, adding wrinkles to the material on a nanoscale. This was achieved by depositing layers of graphene oxide onto a shrink film, then shrunken, with the film dissolved before being shrunken again on another sheet of film. The crumpled graphene became [[Ultrahydrophobicity|superhydrophobic]], and, when used as a battery electrode, the material was shown to have as much as a 400% increase in [[electrochemical]] [[current density]].<ref>{{cite web |last1=Stacey |first1=Kevin |title=Wrinkles and crumples make graphene better {{!}} News from Brown |url=https://news.brown.edu/articles/2016/03/wrinkles |website=news.brown.edu |publisher=Brown University |accessdate=23 June 2016 |archiveurl=https://web.archive.org/web/20160408041658/https://news.brown.edu/articles/2016/03/wrinkles |archivedate=8 April 2016 |language=English |date=21 March 2016}}</ref><ref>{{cite journal |last1=Chen |first1=Po-Yen |last2=Sodhi |first2=Jaskiranjeet |last3=Qiu |first3=Yang |last4=Valentin |first4=Thomas M. |last5=Steinberg |first5=Ruben Spitz |last6=Wang |first6=Zhongying |last7=Hurt |first7=Robert H. |last8=Wong |first8=Ian Y. |title=Multiscale Graphene Topographies Programmed by Sequential Mechanical Deformation |journal=Advanced Materials |volume=28 |issue=18 |publisher=John Wiley & Sons, Inc. |pages=3564–3571 |doi=10.1002/adma.201506194 |pmid=26996525 |date=6 May 2016}}</ref>

==Production==
{{Main|Graphene production techniques}}
A rapidly increasing list of production techniques have been developed to enable graphene's use in commercial applications.<ref>{{cite journal|last1=Backes|first1=Claudia|displayauthors=etal|title=Production and processing of graphene and related materials|journal=2D Materials|volume=7|pages= 022001|date=2020|issue=2|doi=10.1088/2053-1583/ab1e0a|bibcode=2020TDM.....7b2001B|doi-access=free}}</ref>

Isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle, because the rapid growth of [[phonon]] density with increasing lateral size forces 2D crystallites to bend into the third dimension.  In all cases, graphene must bond to a substrate to retain its two-dimensional shape.<ref name="Sciencerev09" />

Small graphene structures, such as graphene quantum dots and nanoribbons, can be produced by "bottom up" methods that assemble the lattice from organic molecule monomers (e. g. citric acid, glucose).  "Top down" methods, on the other hand, cut bulk graphite and graphene materials with strong chemicals (e. g. mixed acids).

===Mechanical===
====Mechanical exfoliation====

Geim and Novoselov initially used [[adhesive tape]] to pull graphene sheets away from graphite. Achieving single layers typically requires multiple exfoliation steps. After exfoliation the flakes are deposited on a silicon wafer. Crystallites larger than 1&nbsp;mm and visible to the naked eye can be obtained.<ref name="PhysTod">{{cite journal |last1=Geim |first1=A. K. |last2=MacDonald |first2=A. H. |title=Graphene: Exploring carbon flatland |journal=Physics Today |volume=60 |pages=35–41 |year=2007 |doi=10.1063/1.2774096 |bibcode=2007PhT....60h..35G |issue=8}}</ref>

As of 2014, exfoliation produced graphene with the lowest number of defects and highest electron mobility.<ref name="arx1406">{{cite arXiv|eprint=1406.0809|class=cond-mat.mtrl-sci|first1=F. V.|last1=Kusmartsev|first2=W. M.|last2=Wu|title=Application of Graphene within Optoelectronic Devices and Transistors|last3=Pierpoint|first3=M. P.|last4=Yung|first4=K. C.|year=2014}}</ref>

Alternatively a [[Wedge based mechanical exfoliation|sharp single-crystal diamond wedge]] penetrates onto the graphite source to cleave layers.<ref name="Jayasena2011">{{cite journal |last=Jayasena |first=Buddhika |author2=Subbiah Sathyan |title=A novel mechanical cleavage method for synthesizing few-layer graphenes |journal=Nanoscale Research Letters |date=2011 |volume=6 |issue=95 |pages=95 |doi=10.1186/1556-276X-6-95 |bibcode=2011NRL.....6...95J |pmid=21711598 |pmc=3212245}}</ref>

In 2014 defect-free, unoxidized graphene-containing liquids were made from graphite using mixers that produce local shear rates greater than {{val|10 |e=4}}.<ref>{{cite web |url=http://www.kurzweilai.net/a-new-method-of-producing-large-volumes-of-high-quality-graphene |title=A new method of producing large volumes of high-quality graphene |publisher=KurzweilAI |date=2 May 2014 |accessdate=3 August 2014}}</ref><ref>{{cite journal |doi=10.1038/nmat3944 |pmid=24747780 |title=Scalable production of large quantities of defect-free few-layer graphene by shear exfoliation in liquids |journal=Nature Materials |date=2014 |volume=13 |issue=6 |pages=624–630 |first=Keith R. |last=Paton |bibcode=2014NatMa..13..624P|hdl=2262/73941 |url=http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf }}</ref>

Shear exfoliation is another method which by using rotor-stator mixer the scalable production of the defect-free Graphene has become possible <ref>{{cite journal |last1=ROUZAFZAY |first1=F. |last2=SHIDPOUR |first2=R. |year=2020 |title=Graphene@ZnO nanocompound for short-time water treatment under sun-simulated irradiation: Effect of shear exfoliation of graphene using kitchen blender on photocatalytic degradation |journal=Alloys and Compounds |volume=829 |pages=154614 |doi=10.1016/J.JALLCOM.2020.154614 }}</ref>

====Ultrasonic exfoliation====

Dispersing graphite in a liquid medium can produce graphene by [[sonication]] followed by [[centrifugation]],<ref name=zhao2014e/><ref>{{Cite journal |last1=Hernandez |first1=Y. |last2=Nicolosi |first2=V. |last3=Lotya |first3=M. |last4=Blighe |first4=F. M. |last5=Sun |first5=Z. |last6=De |first6=S. |last7=McGovern |first7=I. T. |last8=Holland |first8=B. |last9=Byrne |first9=M. |last10=Gun'Ko |first10=Y. K. |last11=Boland |first11=J. J. |last12=Niraj |first12=P. |last13=Duesberg |first13=G. |last14=Krishnamurthy |first14=S. |last15=Goodhue |first15=R. |last16=Hutchison |first16=J. |last17=Scardaci |first17=V. |last18=Ferrari |first18=A. C. |last19=Coleman |first19=J. N. |title=High-yield production of graphene by liquid-phase exfoliation of graphite |doi=10.1038/nnano.2008.215 |journal=Nature Nanotechnology |volume=3 |issue=9 |pages=563–568 |year=2008 |pmid=18772919 |pmc= |arxiv=0805.2850 |bibcode=2008NatNa...3..563H}}</ref> producing concentrations {{val|2.1 |u=mg/ml}} in [[N-methylpyrrolidone]].<ref>{{Cite journal |last1=Alzari |first1=V. |last2=Nuvoli |first2=D. |last3=Scognamillo |first3=S. |last4=Piccinini |first4=M. |last5=Gioffredi |first5=E. |last6=Malucelli |first6=G. |last7=Marceddu |first7=S. |last8=Sechi |first8=M. |last9=Sanna |first9=V. |last10=Mariani |first10=A. |s2cid=27531863 |doi=10.1039/C1JM11076D |title=Graphene-containing thermoresponsive nanocomposite hydrogels of poly(N-isopropylacrylamide) prepared by frontal polymerization |journal=Journal of Materials Chemistry |volume=21 |issue=24 |page=8727 |year=2011 |pmid= |pmc=}}</ref> Using a suitable [[ionic liquid]] as the dispersing liquid medium produced concentrations of {{val|5.33 |u=mg/ml}}.<ref>{{Cite journal |last1=Nuvoli |first1=D. |last2=Valentini |first2=L. |last3=Alzari |first3=V. |last4=Scognamillo |first4=S. |last5=Bon |first5=S. B. |last6=Piccinini |first6=M. |last7=Illescas |first7=J. |last8=Mariani |first8=A. |doi=10.1039/C0JM02461A |title=High concentration few-layer graphene sheets obtained by liquid phase exfoliation of graphite in ionic liquid |journal=Journal of Materials Chemistry |volume=21 |issue=10 |pages=3428–3431 |year=2011 |pmid= |pmc=|arxiv=1010.2859 }}</ref> Restacking is an issue with this technique.

Adding a [[surfactant]] to a solvent prior to sonication prevents restacking by adsorbing to the graphene's surface. This produces a higher graphene concentration, but removing the surfactant requires chemical treatments.{{citation needed|date=April 2014}}

Sonicating graphite at the interface of two [[Miscibility|immiscible]] liquids, most notably [[heptane]] and water, produced macro-scale graphene films. The graphene sheets are adsorbed to the high energy interface between the materials and are kept from restacking. The sheets are up to about 95% transparent and conductive.<ref>{{cite journal |last1=Woltornist |first1=S. J. |last2=Oyer |first2=A. J. |last3=Carrillo |first3=J.-M. Y. |last4=Dobrynin |first4=A. V |last5=Adamson |first5=D. H. |s2cid=27816586 |year=2013 |title=Conductive thin films of pristine graphene by solvent interface trapping |journal=ACS Nano |volume=7 |issue=8 |pages=7062–6 |doi=10.1021/nn402371c|pmid=23879536 }}</ref>

With definite cleavage parameters, the box-shaped graphene (BSG) [[nanostructure]] can be prepared on [[graphite]] [[crystal]].<ref name="stm2016" />

===Splitting monolayer carbon===
====Nanotube slicing====

Graphene can be created by opening [[carbon nanotube]]s by cutting or etching.<ref>{{cite journal |title=Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons |last=Brumfiel |first=G. |journal=Nature |year=2009 |doi=10.1038/news.2009.367}}</ref> In one such method [[MWNT|multi-walled carbon nanotubes]] are cut open in solution by action of [[potassium permanganate]] and [[sulfuric acid]].<ref>{{cite journal |title=Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons |last1=Kosynkin |first1=D. V. |last2=Higginbotham |first2=Amanda L. |last3=Sinitskii |first3=Alexander |last4=Lomeda |first4=Jay R. |last5=Dimiev |first5=Ayrat |last6=Price |first6=B. Katherine |last7=Tour |first7=James M. |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07872 |pmid=19370030 |issue=7240 |bibcode=2009Natur.458..872K |pages=872–6|hdl=10044/1/4321 |hdl-access=free }}</ref><ref>{{cite journal |title=Narrow graphene nanoribbons from carbon nanotubes |last1=Liying |first1=Jiao |first2=Li |last2=Zhang |first3=Xinran |last3=Wang |first4=Georgi |last4=Diankov |first5=Hongjie |last5=Dai |authorlink5=Hongjie Dai |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07919 |pmid=19370031 |issue=7240 |bibcode=2009Natur.458..877J |pages=877–80}}</ref>

====Fullerene splitting====

Another approach sprays [[Buckminsterfullerene|buckyballs]] at supersonic speeds onto a substrate. The balls cracked open upon impact, and the resulting unzipped cages then bond together to form a graphene film.<ref>{{cite web |title=How to Make Graphene Using Supersonic Buckyballs {{!}} MIT Technology Review |url=http://www.technologyreview.com/view/539911/how-to-make-graphene-using-supersonic-buckyballs |website=MIT Technology Review |accessdate=2015-10-11 |date=August 13, 2015}}</ref>

===Chemical===
====Graphite oxide reduction====

P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name=grtim2009/><ref>{{cite web|url=http://www.aps.org/publications/apsnews/201001/letters.cfm|title=Many Pioneers in Graphene Discovery|last=Geim|first=Andre|date=January 2010|work=Letters to the Editor|publisher=American Physical Society|url-status=live|archive-url=|archive-date=|access-date=2019-11-10}}</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes.

Another method is reduction of graphite oxide monolayer films, e.g. by [[hydrazine]] with [[annealing (metallurgy)|annealing]] in [[argon]]/[[hydrogen]] with an almost intact carbon framework that allows efficient removal of functional groups. Measured [[charge carrier]] mobility exceeded {{convert|1000|cm|2}}/Vs.<ref name="Eigler2013">{{cite journal |first1=S. |last1=Eigler |first2=M. |last2=Enzelberger-Heim |first3=S. |last3=Grimm |first4=P. |last4=Hofmann |first5=W. |last5=Kroener |first6=A. |last6=Geworski |first7=C. |last7=Dotzer |first8=M. |last8=Röckert |first9=J. |last9=Xiao |first10=C. |last10=Papp |first11=O. |last11=Lytken |first12=H.-P. |last12=Steinrück |first13=P. |last13=Müller |first14=A. |last14=Hirsch |title=Wet Chemical Synthesis of Graphene |journal=Advanced Materials |volume=25 |issue=26 |year=2013 |pages=3583–3587 |doi=10.1002/adma.201300155 |pmid=23703794}}</ref>

Burning a graphite oxide coated [[DVD]] produced a conductive graphene film (1738 siemens per meter) and specific surface area (1520 square meters per gram) that was highly resistant and malleable.<ref>{{cite journal |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |journal=Science |volume=335 |issue=6074 |pages=1326–1330 |date=16 March 2012 |doi=10.1126/science.1216744 |pmid=22422977 |last1=El-Kady |first1=M. F. |last2=Strong |first2=V. |last3=Dubin |first3=S. |last4=Kaner |first4=R. B. |s2cid=18958488 |bibcode=2012Sci...335.1326E }}<br/>{{cite web |last=Marcus |first=Jennifer |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |title=Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=15 March 2012 |access-date=20 March 2012 |archive-url=https://www.webcitation.org/6HPJaTQQj?url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |archive-date=16 June 2013 |url-status=dead }}</ref>

A dispersed reduced graphene oxide suspension was synthesized in water by a hydrothermal dehydration method without using any surfactant. The approach is facile, industrially applicable, environmentally friendly and cost effective. Viscosity measurements confirmed that the graphene colloidal suspension (Graphene nanofluid) exhibit Newtonian behavior, with the viscosity showing close resemblance to that of water.<ref>{{cite journal |last1=Sadri |first1=R. |s2cid=53349683 |title=Experimental study on thermo-physical and rheological properties of stable and green reduced graphene oxide nanofluids: Hydrothermal assisted technique |journal=Journal of Dispersion Science and Technology |date=15 Feb 2017 |volume=38 |issue=9 |pages=1302–1310 |doi=10.1080/01932691.2016.1234387 }}</ref>

===Molten salts===
Graphite particles can be corroded in molten salts to form a variety of carbon nanostructures including graphene.<ref>{{cite journal |first1=A.R. |last1=Kamali |first2=D.J. |last2=Fray |journal=Carbon |volume=56 |pages=121–131 |doi=10.1016/j.carbon.2012.12.076 |title=Molten salt corrosion of graphite as a possible way to make carbon nanostructures|year=2013 }}</ref> Hydrogen cations, dissolved in molten lithium chloride, can be discharged on cathodically polarized graphite rods, which then intercalate, peeling graphene sheets. The graphene nanosheets produced displayed a single-crystalline structure with a lateral size of several hundred nanometers and a high degree of crystallinity and thermal stability.<ref>{{cite journal |last1=Kamali |first1=D.J.Fray |year= 2015|title=Large-scale preparation of graphene by high temperature insertion of hydrogen into graphite |url= |journal=Nanoscale |volume=7 |issue= 26|pages=11310–11320 |doi=10.1039/C5NR01132A|pmid=26053881 |doi-access=free }}</ref>

===Electrochemical synthesis===

Electrochemical synthesis can exfoliate graphene. Varying a pulsed voltage controls thickness, flake area, number of defects and affects its properties. The process begins by bathing the graphite in a solvent for intercalation. The process can be tracked by monitoring the solution's transparency with an LED and photodiode.
<ref>{{cite web |title=How to tune graphene properties by introducing defects {{!}} KurzweilAI |url=http://www.kurzweilai.net/how-to-tune-graphene-properties-by-introducing-defects |website=www.kurzweilai.net |accessdate=2015-10-11 |date=July 30, 2015}}</ref><ref>{{Cite journal |title=Controlling the properties of graphene produced by electrochemical exfoliation - IOPscience |date=2015-08-21 |doi=10.1088/0957-4484/26/33/335607 |pmid=26221914 |first1=Mario |last1=Hofmann |first2=Wan-Yu |last2=Chiang |first3=Tuân D |last3=Nguyễn |first4=Ya-Ping |last4=Hsieh |s2cid=206072084 |volume=26 |issue=33 |journal=Nanotechnology |page=335607 |bibcode=2015Nanot..26G5607H}}</ref>

===Hydrothermal self-assembly===
Graphene has been prepared by using a sugar (e.g. [[glucose]], [[sugar]], [[fructose]], etc.) This substrate-free "bottom-up" synthesis is safer, simpler and more environmentally friendly than exfoliation. The method can control thickness, ranging from monolayer to multilayers, which is known as "Tang-Lau Method".<ref name="r1">{{cite journal |last1=Tang |first1=L. |last2=Li |first2=X. |last3=Ji |first3=R. |last4=Teng |first4=K. S. |last5=Tai |first5=G. |last6=Ye |first6=J. |last7=Wei |first7=C. |last8=Lau |first8=S. P. |doi=10.1039/C2JM15944A |title=Bottom-up synthesis of large-scale graphene oxide nanosheets |journal=Journal of Materials Chemistry |volume=22 |issue=12 |page=5676 |year=2012 |pmid= |pmc=}}</ref><ref name=lixu2013/><ref name=lili2013b/><ref name=lixu2014/>

===Thermal decomposition of silicon carbide===
Heating [[silicon carbide]] (SiC) to high temperatures ({{val|1100 |u=°C}}) under low pressures (c. 10<sup>−6</sup> torr) reduces it to graphene.<ref name="0908.1900">{{cite journal |first1=Johannes |last1=Jobst |first2=Daniel |last2=Waldmann |first3=Florian |last3=Speck |first4=Roland |last4=Hirner |first5=Duncan K. |last5=Maude |first6=Thomas |last6=Seyller |first7=Heiko B. |last7=Weber |title=How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect |year=2009 |doi=10.1103/PhysRevB.81.195434 |journal=Physical Review B |volume=81 |issue=19 |page=195434 |arxiv=0908.1900 |bibcode=2010PhRvB..81s5434J}}</ref><ref name="ShenAPL">{{cite journal |first1=T. |last1=Shen |first2=J.J. |last2=Gu |first3=M |last3=Xu |first4=Y.Q. |last4=Wu |first5=M.L. |last5=Bolen |first6=M.A. |last6=Capano |first7=L.W. |last7=Engel |first8=P.D. |last8=Ye |title=Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001) |doi=10.1063/1.3254329 |journal=Applied Physics Letters |bibcode=2009ApPhL..95q2105S |year=2009 |volume=95 |issue=17 |page=172105 |arxiv=0908.3822}}</ref><ref name="0909.2903">{{cite journal |first1=Xiaosong |last1=Wu |first2=Yike |last2=Hu |first3=Ming |last3=Ruan |first4=Nerasoa K |last4=Madiomanana |first5=John |last5=Hankinson |first6=Mike |last6=Sprinkle |first7=Claire |last7=Berger |first8=Walt A. |last8=de Heer |year=2009 |title=Half integer quantum Hall effect in high mobility single layer epitaxial graphene |doi=10.1063/1.3266524 |journal=Applied Physics Letters |volume=95 |issue=22 |page=223108 |arxiv=0909.2903 |bibcode=2009ApPhL..95v3108W}}</ref><ref name="0909.1193">{{cite journal |first1=Samuel |last1=Lara-Avila |first2=Alexei |last2=Kalaboukhov |first3=Sara |last3=Paolillo |first4=Mikael |last4=Syväjärvi |first5=Rositza |last5=Yakimova |first6=Vladimir |last6=Fal'ko |first7=Alexander |last7=Tzalenchuk |first8=Sergey |last8=Kubatkin |title=SiC Graphene Suitable For Quantum Hall Resistance Metrology |journal=Science Brevia |date=7 July 2009 |arxiv=0909.1193 |doi=<!-- none --> |bibcode=2009arXiv0909.1193L |pmid=<!-- none -->}}</ref><ref name="phase1">{{cite journal |first1=J.A. |last1=Alexander-Webber |first2=A.M.R. |last2=Baker |first3=T.J.B.M. |last3=Janssen |first4=A. |last4=Tzalenchuk |first5=S. |last5=Lara-Avila |first6=S. |last6=Kubatkin |first7=R. |last7=Yakimova |first8=B. A. |last8=Piot |first9=D. K. |last9=Maude |first10=R.J. |last10=Nicholas |year=2013 |title=Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene |doi=10.1103/PhysRevLett.111.096601 |journal=Physical Review Letters |volume=111 |issue=9 |page=096601 |pmid=24033057 |arxiv=1304.4897 |bibcode=2013PhRvL.111i6601A}}</ref><ref>{{cite journal |last=Sutter |first=P. |title=Epitaxial graphene: How silicon leaves the scene |journal=Nature Materials |volume=8 |year=2009 |pmid=19229263 |doi=10.1038/nmat2392 |issue=3 |bibcode=2009NatMa...8..171S |pages=171–2|url=https://zenodo.org/record/1233465 }}</ref>

===Chemical vapor deposition===

====Epitaxy====

[[Epitaxial graphene growth on silicon carbide]] is wafer-scale technique to produce graphene. [[Epitaxy|Epitaxial]] graphene may be coupled to surfaces weakly enough (by [[Van der Waals force]]s) to retain the two dimensional [[electronic band structure]] of isolated graphene.<ref name=Gall1>{{cite journal |last1=Gall |first1=N. R. |last2=Rut'Kov |first2=E. V. |last3=Tontegode |first3=A. Ya. |year=1997 |title=Two Dimensional Graphite Films on Metals and Their Intercalation |journal=[[International Journal of Modern Physics B]] |volume=11 |issue=16 |pages=1865–1911 |bibcode=1997IJMPB..11.1865G |doi=10.1142/S0217979297000976}}</ref>

A normal [[silicon wafer]] coated with a layer of [[germanium]] (Ge) dipped in dilute [[hydrofluoric acid]] strips the naturally forming [[germanium oxide]] groups, creating hydrogen-terminated germanium. CVD can coat that with graphene.<ref>{{cite web |url=http://www.extremetech.com/extreme/179874-samsungs-graphene-breakthrough-could-finally-put-the-wonder-material-into-real-world-devices |title=Samsung's graphene breakthrough could finally put the wonder material into real-world devices |publisher=ExtremeTech |date=7 April 2014 |accessdate=13 April 2014}}</ref><ref>{{cite journal |doi=10.1126/science.1252268 |pmid=24700471 |title=Wafer-Scale Growth of Single-Crystal Monolayer Graphene on Reusable Hydrogen-Terminated Germanium |journal=Science |volume=344 |issue=6181 |pages=286–9 |year=2014 |last1=Lee |first1=J.-H. |last2=Lee |first2=E. K. |last3=Joo |first3=W.-J. |last4=Jang |first4=Y. |last5=Kim |first5=B.-S. |last6=Lim |first6=J. Y. |last7=Choi |first7=S.-H. |last8=Ahn |first8=S. J. |last9=Ahn |first9=J. R. |last10=Park |first10=M.-H. |last11=Yang |first11=C.-W. |last12=Choi |first12=B. L. |last13=Hwang |first13=S.-W. |last14=Whang |first14=D. |bibcode=2014Sci...344..286L}}</ref>

The direct synthesis of graphene on insulator TiO<sub>2</sub> with high-dielectric-constant (high-κ). A two-step CVD process is shown to grow graphene directly on TiO<sub>2</sub> crystals or exfoliated TiO<sub>2</sub> nanosheets without using any metal catalyst.<ref>{{cite journal|last1=Bansal|first1=Tanesh|last2=Durcan|first2=Christopher A. |last3=Jain|first3=Nikhil|last4=Jacobs-Gedrim|first4=Robin B.|last5=Xu|first5=Yang|last6=Yu|first6=Bin|title=Synthesis of few-to-monolayer graphene on rutile titanium dioxide|journal=Carbon|volume=55|pages=168–175|date=2013|doi=10.1016/j.carbon.2012.12.023}}</ref>

====Metal substrates====

CVD graphene can be grown on metal substrates including ruthenium,<ref name="PhysOrg.com">{{cite news |title=A smarter way to grow graphene |url=http://www.physorg.com/news129980833.html |publisher=PhysOrg.com |date=May 2008}}</ref> iridium,<ref name="grIr111">{{cite journal |last1=Pletikosić |first1=I. |last2=Kralj |first2=M. |last3=Pervan |first3=P. |last4=Brako |first4=R. |last5=Coraux |first5=J. |last6=n'Diaye |first6=A. |last7=Busse |first7=C. |last8=Michely |first8=T. |year=2009 |title=Dirac Cones and Minigaps for Graphene on Ir(111) |journal=Physical Review Letters |volume=102 |page=056808 |doi=10.1103/PhysRevLett.102.056808 |pmid=19257540 |bibcode=2009PhRvL.102e6808P |issue=5 |arxiv=0807.2770}}</ref> nickel<ref>{{cite web |url=http://www.gizmag.com/graphene-glass-substrate-deposition/32271 |title=New process could lead to more widespread use of graphene |publisher=Gizmag.com |date= 28 May 2014|accessdate=14 June 2014}}</ref> and copper<ref>{{Cite journal|last1=Liu|first1=W.|last2=Li|first2=H.|last3=Xu|first3=C.|last4=Khatami|first4=Y.|last5=Banerjee|first5=K.|year=2011|title=Synthesis of high-quality monolayer and bilayer graphene on copper using chemical vapor deposition|url=https://www.sciencedirect.com/science/article/abs/pii/S0008622311004106|journal=Carbon|volume=49|issue=13|pages=4122–4130|doi=10.1016/j.carbon.2011.05.047|via=}}</ref><ref>{{cite journal |last1=Mattevi |first1=Cecilia |last2=Kim |first2=Hokwon |last3=Chhowalla |first3=Manish |s2cid=213144 |title=A review of chemical vapour deposition of graphene on copper |journal=Journal of Materials Chemistry |date=2011 |volume=21 |issue=10 |pages=3324–3334 |doi=10.1039/C0JM02126A}}</ref>

====Sodium ethoxide pyrolysis====

Gram-quantities were produced by the reduction of [[ethanol]] by [[sodium]] metal, followed by [[pyrolysis]] and washing with water.<ref>{{cite journal |doi=10.1038/nnano.2008.365 |title=Gram-scale production of graphene based on solvothermal synthesis and sonication |year=2008 |last1=Choucair |first1=M. |last2=Thordarson |first2=P |last3=Stride |first3=JA |journal=Nature Nanotechnology |pmid=19119279 |volume=4 |issue=1 |pages=30–3 |bibcode=2009NatNa...4...30C}}</ref>

====Roll-to-roll====
In 2014 a two-step roll-to-roll manufacturing process was announced. The first roll-to-roll step produces the graphene via chemical vapor deposition. The second step binds the graphene to a substrate.<ref>{{cite web |url=http://www.purdue.edu/newsroom/releases/2014/Q3/purdue-based-startup-scales-up-graphene-production,-develops-biosensors-and-supercapacitors.html |title=Purdue-based startup scales up graphene production, develops biosensors and supercapacitors |date=18 September 2014 |accessdate=4 October 2014 |publisher=Purdue University |last=Martin |first=Steve}}</ref><ref>{{Cite news |url=http://www.rdmag.com/videos/2014/09/startup-scales-graphene-production-develops-biosensors-and-supercapacitors |title=Startup scales up graphene production, develops biosensors and supercapacitors |date=19 September 2014 |work=R&D Magazine |accessdate=4 October 2014}}</ref>
[[File:Wafer Scale CVD Graphene Raman Mapping.gif|thumb|upright=1.3|Large-area Raman mapping of CVD graphene on deposited Cu thin film on 150 mm SiO<sub>2</sub>/Si wafers reveals >95% monolayer continuity and an average value of ∼2.62 for ''I''<sub>2D</sub>/''I''<sub>G</sub>. The scale bar is 200 μm.]]

====Cold wall====
Growing graphene in an industrial resistive-heating cold wall CVD system was claimed to produce graphene 100 times faster than conventional CVD systems, cut costs by 99% and produce material with enhanced electronic qualities.<ref>{{cite web |title=New process could usher in "graphene-driven industrial revolution" |url=http://www.gizmag.com/graphene-low-cost-nanocvd/38195 |website=www.gizmag.com |accessdate=2015-10-05 |first=Darren |last=Quick |date=June 26, 2015}}</ref><ref>{{Cite journal |title=High Quality Monolayer Graphene Synthesized by Resistive Heating Cold Wall Chemical Vapor Deposition |journal=Advanced Materials |date=2015-07-01 |issn=1521-4095 |pages=4200–4206 |volume=27 |issue=28 |doi=10.1002/adma.201501600 |pmid=26053564 |pmc=4744682 |first1=Thomas H. |last1=Bointon |first2=Matthew D. |last2=Barnes |first3=Saverio |last3=Russo |first4=Monica F. |last4=Craciun|bibcode=2015arXiv150608569B |arxiv=1506.08569 }}</ref>

=====Wafer scale CVD graphene=====
CVD graphene is scalable and has been grown on deposited Cu thin film catalyst on 100 to 300&nbsp;mm standard Si/SiO<sub>2</sub> wafers<ref>{{Cite journal |last1=Tao |first1=Li |last2=Lee |first2=Jongho |last3=Chou |first3=Harry |last4=Holt |first4=Milo |last5=Ruoff |first5=Rodney S. |last6=Akinwande |first6=Deji |s2cid=30130350 |date=2012-03-27 |title=Synthesis of High Quality Monolayer Graphene at Reduced Temperature on Hydrogen-Enriched Evaporated Copper (111) Films |journal=ACS Nano |volume=6 |issue=3 |pages=2319–2325 |doi=10.1021/nn205068n |pmid=22314052 |issn=1936-0851}}</ref><ref name=":3">{{Cite journal |last1=Tao |first1=Li |last2=Lee |first2=Jongho |last3=Holt |first3=Milo |last4=Chou |first4=Harry |last5=McDonnell |first5=Stephen J. |last6=Ferrer |first6=Domingo A. |last7=Babenco |first7=Matías G. |last8=Wallace |first8=Robert M. |last9=Banerjee |first9=Sanjay K. |s2cid=55726071 |date=2012-11-15 |title=Uniform Wafer-Scale Chemical Vapor Deposition of Graphene on Evaporated Cu (111) Film with Quality Comparable to Exfoliated Monolayer |journal=The Journal of Physical Chemistry C |volume=116 |issue=45 |pages=24068–24074 |doi=10.1021/jp3068848 |issn=1932-7447}}</ref><ref name=":4">{{Cite journal |last1=Rahimi |first1=Somayyeh |last2=Tao |first2=Li |last3=Chowdhury |first3=Sk. Fahad |last4=Park |first4=Saungeun |last5=Jouvray |first5=Alex |last6=Buttress |first6=Simon |last7=Rupesinghe |first7=Nalin |last8=Teo |first8=Ken |last9=Akinwande |first9=Deji |date=2014-10-28 |title=Toward 300 mm Wafer-Scalable High-Performance Polycrystalline Chemical Vapor Deposited Graphene Transistors |journal=ACS Nano |volume=8 |issue=10 |pages=10471–10479 |doi=10.1021/nn5038493 |pmid=25198884 |issn=1936-0851}}</ref> on an Axitron Black Magic system. Monolayer graphene coverage of >95% is achieved on 100 to 300&nbsp;mm wafer substrates with negligible defects, confirmed by extensive Raman mapping.<ref name=":3" /><ref name=":4" />

===Carbon dioxide reduction===

A highly exothermic reaction combusts [[magnesium]] in an oxidation–reduction reaction with carbon dioxide, producing carbon nanoparticles including graphene and [[fullerene]]s.<ref>{{Cite journal |last1=Chakrabarti |first1=A. |last2=Lu |first2=J. |last3=Skrabutenas |first3=J. C. |last4=Xu |first4=T. |last5=Xiao |first5=Z. |last6=Maguire |first6=J. A. |last7=Hosmane |first7=N. S. |s2cid=96850993 |doi=10.1039/C1JM11227A |title=Conversion of carbon dioxide to few-layer graphene |journal=Journal of Materials Chemistry |volume=21 |issue=26 |page=9491 |year=2011 |pmid= |pmc=}}</ref>

===Spin coating===

In 2014, carbon nanotube-reinforced graphene was made via spin coating and annealing functionalized carbon nanotubes.<ref name="kurz5011"/>

===Supersonic spray===

Supersonic acceleration of droplets through a [[Laval nozzle]] was used to deposit reduced graphene-oxide on a substrate. The energy of the impact rearranges that carbon atoms into flawless graphene.<ref>{{Cite journal |doi=10.1002/adfm.201400732 |title=Self-Healing Reduced Graphene Oxide Films by Supersonic Kinetic Spraying |journal=Advanced Functional Materials |volume=24 |issue=31 |pages=4986–4995 |year=2014 |last1=Kim |first1=D. Y. |last2=Sinha-Ray |first2=S. |last3=Park |first3=J. J. |last4=Lee |first4=J. G. |last5=Cha |first5=Y. H. |last6=Bae |first6=S. H. |last7=Ahn |first7=J. H. |last8=Jung |first8=Y. C. |last9=Kim |first9=S. M. |last10=Yarin |first10=A. L. |last11=Yoon |first11=S. S.}}</ref><ref>{{cite journal |url=http://www.kurzweilai.net/supersonic-spray-creates-high-quality-graphene-layer |title=Supersonic spray creates high-quality graphene layer |journal=Advanced Functional Materials |volume=24 |issue=31 |pages=4986–4995 |doi=10.1002/adfm.201400732 |publisher=KurzweilAI |accessdate=14 June 2014 |year=2014 |last1=Kim |first1=Do-Yeon |last2=Sinha-Ray |first2=Suman |last3=Park |first3=Jung-Jae |last4=Lee |first4=Jong-Gun |last5=Cha |first5=You-Hong |last6=Bae |first6=Sang-Hoon |last7=Ahn |first7=Jong-Hyun |last8=Jung |first8=Yong Chae |last9=Kim |first9=Soo Min |last10=Yarin |first10=Alexander L. |last11=Yoon |first11=Sam S.}}</ref>

===Laser===

In 2014 a {{chem|CO|2}} [[infrared laser]] produced and patterned porous three-dimensional graphene film networks from commercial polymer films. The result exhibits high electrical conductivity. Laser-induced production appeared to allow roll-to-roll manufacturing processes.<ref>{{Cite journal |doi=10.1038/ncomms6714 |pmid=25493446 |pmc=4264682 |title=Laser-induced porous graphene films from commercial polymers |journal=Nature Communications |volume=5 |page=5714 |year=2014 |last1=Lin |first1=J. |last2=Peng |first2=Z. |last3=Liu |first3=Y. |last4=Ruiz-Zepeda |first4=F. |last5=Ye |first5=R. |last6=Samuel |first6=E. L. G. |last7=Yacaman |first7=M. J. |last8=Yakobson |first8=B. I. |last9=Tour |first9=J. M. |bibcode=2014NatCo...5.5714L}}</ref>

===Microwave-assisted oxidation===
In 2012, microwave energy was reported to directly synthesize graphene in one step.<ref>{{Cite journal |title=Microwave- and Nitronium Ion-Enabled Rapid and Direct Production of Highly Conductive Low-Oxygen Graphene |journal=Journal of the American Chemical Society |date=2012-04-04 |issn=0002-7863 |pages=5850–5856 |volume=134 |issue=13 |doi=10.1021/ja210725p |pmid=22385480 |first1=Pui Lam |last1=Chiu |first2=Daniel D. T. |last2=Mastrogiovanni |first3=Dongguang |last3=Wei |first4=Cassandre |last4=Louis |first5=Min |last5=Jeong |first6=Guo |last6=Yu |first7=Peter |last7=Saad |first8=Carol R. |last8=Flach |first9=Richard |last9=Mendelsohn|s2cid=11991071 }}</ref> This approach avoids use of potassium permanganate in the reaction mixture. It was also reported that by microwave radiation assistance, graphene oxide with or without holes can be synthesized by controlling microwave time.<ref>{{cite journal |doi=10.1002/smll.201403402 |pmid=25683019 |title=Microwave Enabled One-Pot, One-Step Fabrication and Nitrogen Doping of Holey Graphene Oxide for Catalytic Applications |journal=Small |volume=11 |issue=27 |pages=3358–68 |year=2015 |last1=Patel |first1=Mehulkumar |last2=Feng |first2=Wenchun |last3=Savaram |first3=Keerthi |last4=Khoshi |first4=M. Reza |last5=Huang |first5=Ruiming |last6=Sun |first6=Jing |last7=Rabie |first7=Emann |last8=Flach |first8=Carol |last9=Mendelsohn |first9=Richard |last10=Garfunkel |first10=Eric |last11=He |first11=Huixin|s2cid=14567874 }}</ref> Microwave heating can dramatically shorten the reaction time from days to seconds.

Graphene can also me made by [[microwave radiation|microwave]] assisted hydrothermal pyrolysis<ref name=tang2014/><ref name=tang2012/>

===Ion implantation===
Accelerating carbon ions inside an electrical field into a semiconductor made of thin nickel films on a substrate of SiO<sub>2</sub>/Si, creates a wafer-scale ({{Convert|4|in}}) wrinkle/tear/residue-free graphene layer at a relatively low temperature of 500&nbsp;°C.<ref>{{cite web |title=Korean researchers grow wafer-scale graphene on a silicon substrate {{!}} KurzweilAI |url=http://www.kurzweilai.net/korean-researchers-grow-wafer-scale-graphene-on-a-silicon-substrate |website=www.kurzweilai.net |accessdate=2015-10-11 |date=July 21, 2015}}</ref><ref>{{Cite journal |title=Wafer-scale synthesis of multi-layer graphene by high-temperature carbon ion implantation |journal=Applied Physics Letters |date=2015-07-20 |issn=0003-6951 |page=033104 |volume=107 |issue=3 |doi=10.1063/1.4926605 |first1=Janghyuk |last1=Kim |first2=Geonyeop |last2=Lee |first3=Jihyun |last3=Kim |bibcode=2015ApPhL.107c3104K}}</ref>

=== CMOS-compatible graphene ===
Integration of graphene in the widely employed [[Semiconductor device fabrication|CMOS fabrication process]] demands its transfer-free direct synthesis on [[dielectric]] substrates at temperatures below 500&nbsp;°C. At the [[International Electron Devices Meeting|IEDM]] 2018, researchers from [[University of California, Santa Barbara]], demonstrated a novel CMOS-compatible graphene synthesis process at 300&nbsp;°C suitable for back-end-of-line ([[Back end of line|BEOL]]) applications.<ref>{{Cite journal|last=Thomas|first=Stuart|date=2018|title=CMOS-compatible graphene|url=https://www.nature.com/articles/s41928-018-0178-x|journal=Nature Electronics|volume=1|issue=12|pages=612|doi=10.1038/s41928-018-0178-x|via=}}</ref><ref>{{Cite journal|last1=Jiang|first1=J.|last2=Chu|first2=J. H.|last3=Banerjee|first3=K.|date=2018|title=CMOS-compatible doped-multilayer-graphene interconnects for next-generation VLSI|journal=IEEE International Electron Devices Meeting (IEDM)|volume=|pages=34.5.1–34.5.4|doi=10.1109/IEDM.2018.8614535|isbn=978-1-7281-1987-8}}</ref><ref>{{Cite news|last=|first=|url=https://www.news.ucsb.edu/2019/019563/graphene-goes-mainstream|title=Graphene goes mainstream|date=July 23, 2019|work=The Current, UC Santa Barbara|access-date=|url-status=live}}</ref> The process involves pressure-assisted solid-state [[diffusion]] of [[carbon]] through a [[Thin film|thin-film]] of metal catalyst. The synthesized large-area graphene films were shown to exhibit high-quality (via [[Raman spectroscopy|Raman]] characterization) and similar [[Electrical resistivity and conductivity|resistivity]] values when compared with high-temperature CVD synthesized graphene films of same cross-section down to widths of 20 [[Nanometre|nm]].

==Simulation==
In addition to experimental investigation of graphene and graphene-based devices, their numerical modeling and simulation have been an important research topic. The Kubo formula provides an analytic expression for the graphene's conductivity and shows that it is a function of several physical parameters including wavelength, temperature, and chemical potential.<ref>{{cite journal |last1=Gusynin |first1=V P |last2=Sharapov |first2=S G |last3=Carbotte |first3=J P |title=Magneto-optical conductivity in graphene |journal=Journal of Physics: Condensed Matter |date=17 January 2007 |volume=19 |issue=2 |pages=026222 |doi=10.1088/0953-8984/19/2/026222|arxiv=0705.3783 |bibcode=2007JPCM...19b6222G }}</ref> Moreover, a surface conductivity model, which describes graphene as an infinitesimally thin (two sided) sheet with a local and isotropic conductivity, has been proposed. This model permits derivation of analytical expressions for the electromagnetic field in the presence of a graphene sheet in terms of a dyadic Green function (represented using Sommerfeld integrals) and exciting electric current.<ref>{{cite journal |last1=Hanson |first1=George W. |title=Dyadic Green's Functions for an Anisotropic, Non-Local Model of Biased Graphene |journal=IEEE Transactions on Antennas and Propagation |date=March 2008 |volume=56 |issue=3 |pages=747–757 |doi=10.1109/TAP.2008.917005|bibcode=2008ITAP...56..747H }}</ref> Even though these analytical models and methods can provide results for several canonical problems for benchmarking purposes, many practical problems involving graphene, such as design of arbitrarily shaped electromagnetic devices, are analytically intractable. With the recent advances in the field of computational electromagnetics (CEM), various accurate and efficient numerical methods have become available for analysis of electromagnetic field/wave interactions on graphene sheets and/or graphene-based devices. A comprehensive summary of computational tools developed for analyzing graphene-based devices/systems is proposed.<ref>{{cite journal |last1=Niu |first1=Kaikun |last2=Li |first2=Ping |last3=Huang |first3=Zhixiang |last4=Jiang |first4=Li Jun |last5=Bagci |first5=Hakan |title=Numerical Methods for Electromagnetic Modeling of Graphene: A Review |journal=IEEE Journal on Multiscale and Multiphysics Computational Techniques |date=2020 |volume=5 |pages=44–58 |doi=10.1109/JMMCT.2020.2983336 |hdl=10754/662399 |hdl-access=free }}</ref>

==Graphene analogs==
Graphene analogs<ref>{{Cite journal |title=Artificial honeycomb lattices for electrons, atoms and photons |journal=Nature Nanotechnology |date=2013-09-01 |issn=1748-3387 |pages=625–633 |volume=8 |issue=9 |doi=10.1038/nnano.2013.161 |pmid=24002076 |first1=Marco |last1=Polini |first2=Francisco |last2=Guinea |first3=Maciej |last3=Lewenstein |first4=Hari C. |last4=Manoharan |first5=Vittorio |last5=Pellegrini |arxiv=1304.0750 |bibcode=2013NatNa...8..625P}}</ref> (also referred to as "artificial graphene") are two-dimensional systems which exhibit similar properties to graphene. Graphene analogs are studied intensively since the discovery of graphene in 2004. People try to develop systems in which the physics is easier to observe and to manipulate than in graphene. In those systems, electrons are not always the particles which are used. They might be optical photons,<ref>{{Cite journal |title=Observation of unconventional edge states in 'photonic graphene' |journal=Nature Materials |date=2014-01-01 |issn=1476-1122 |pages=57–62 |volume=13 |issue=1 |doi=10.1038/nmat3783 |pmid=24193661 |first1=Yonatan |last1=Plotnik |first2=Mikael C. |last2=Rechtsman |first3=Daohong |last3=Song |first4=Matthias |last4=Heinrich |first5=Julia M. |last5=Zeuner |first6=Stefan |last6=Nolte |first7=Yaakov |last7=Lumer |first8=Natalia |last8=Malkova |first9=Jingjun |last9=Xu |bibcode=2014NatMa..13...57P|arxiv=1210.5361 }}</ref> microwave photons,<ref>{{Cite journal |title=Topological Transition of Dirac Points in a Microwave Experiment |journal=Physical Review Letters |date=2013-01-14 |page=033902 |volume=110 |issue=3 |doi=10.1103/PhysRevLett.110.033902 |pmid=23373925 |first1=Matthieu |last1=Bellec |first2=Ulrich |last2=Kuhl |first3=Gilles |last3=Montambaux |first4=Fabrice |last4=Mortessagne |arxiv=1210.4642 |bibcode=2013PhRvL.110c3902B}}</ref> plasmons,<ref>{{Cite journal |title=Plasmon Coupling in Self-Assembled Gold Nanoparticle-Based Honeycomb Islands |journal=The Journal of Physical Chemistry C |date=2013-09-12 |issn=1932-7447 |pages=18634–18641 |volume=117 |issue=36 |doi=10.1021/jp405560t |first1=Sebastian P. |last1=Scheeler |first2=Stefan |last2=Mühlig |first3=Carsten |last3=Rockstuhl |first4=Shakeeb Bin |last4=Hasan |first5=Simon |last5=Ullrich |first6=Frank |last6=Neubrech |first7=Stefan |last7=Kudera |first8=Claudia |last8=Pacholski}}</ref> microcavity polaritons,<ref>{{Cite journal |title=Direct Observation of Dirac Cones and a Flatband in a Honeycomb Lattice for Polaritons |journal=Physical Review Letters |date=2014-03-18 |page=116402 |volume=112 |issue=11 |doi=10.1103/PhysRevLett.112.116402 |pmid=24702392 |first1=T. |last1=Jacqmin |first2=I. |last2=Carusotto |first3=I. |last3=Sagnes |first4=M. |last4=Abbarchi |first5=D. D. |last5=Solnyshkov |first6=G. |last6=Malpuech |first7=E. |last7=Galopin |first8=A. |last8=Lemaître |first9=J. |last9=Bloch |arxiv=1310.8105 |bibcode=2014PhRvL.112k6402J}}</ref> or even atoms.<ref>{{cite journal |title= Multi-component quantum gases in spin-dependent hexagonal lattices|issue=5 |pages=434–440 |journal=Nature Physics |volume=7 |doi=10.1038/nphys1916 |date=May 2011 |last1=Sengstock |first1=K. |last2=Lewenstein |first2=M. |last3=Windpassinger |first3=P. |last4=Becker |first4=C. |last5=Meineke |first5=G. |last6=Plenkers |first6=W. |last7=Bick |first7=A. |last8=Hauke |first8=P. |last9=Struck |first9=J. |last10=Soltan-Panahi |first10=P. |bibcode=2011NatPh...7..434S |arxiv=1005.1276 }}</ref> Also, the honeycomb structure in which those particles evolve can be of a different nature than carbon atoms in graphene. It can be, respectively, a [[photonic crystal]], an array of [[metallic rods]], [[metallic nanoparticles]], a lattice of [[coupled microcavities]], or an [[optical lattice]].

==Applications==
{{main|Potential applications of graphene}}
[[File:Graphene Touch Screen.png|thumb|upright=1.5|(a) The typical structure of a touch sensor in a touch panel. (Image courtesy of Synaptics, Incorporated.) (b) An actual example of 2D Carbon Graphene Material Co.,Ltd's graphene transparent conductor-based touchscreen that is employed in (c) a commercial smartphone.]]
Graphene is a transparent and flexible conductor that holds great promise for various material/device applications, including solar cells,<ref>{{cite journal|last1= Zhong|first1=Mengyao|last2=Xu|first2=Dikai|last3=Yu|first3=Xuegong|last4=Huang|first4=Kun|last5=Liu|first5=Xuemei|last6=Xu|first6=Yang|last7=Yang|first7=Deren|title=Interface coupling in graphene/fluorographene heterostructure for high-performance graphene/silicon solar cells|journal=Nano Energy|volume=28|pages=12–18|date=2016|doi=10.1016/j.nanoen.2016.08.031|url= http://xueshu.baidu.com/s?wd=paperuri%3A%28214c0054860ae811a79dc548b3af94f0%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS2211285516303184&ie=utf-8&sc_us=16735334862677938961}}</ref> light-emitting diodes (LED), touch panels, and smart windows or phones.<ref>{{Cite journal |last1=Akinwande |first1=D. |last2=Tao |first2=L. |last3=Yu |first3=Q. |last4=Lou |first4=X. |last5=Peng |first5=P. |last6=Kuzum |first6=D. |date=2015-09-01 |title=Large-Area Graphene Electrodes: Using CVD to facilitate applications in commercial touchscreens, flexible nanoelectronics, and neural interfaces. |journal=IEEE Nanotechnology Magazine |volume=9 |issue=3 |pages=6–14 |doi=10.1109/MNANO.2015.2441105 |issn=1932-4510}}</ref> Smartphone products with graphene touch screens are already on the market.

In 2013, Head announced their new range of graphene tennis racquets.<ref>{{Cite news|url=http://www.tennis.com/gear/2015/02/racquet-review-head-graphene-xt-speed-pro/53947/|title=Racquet Review: Head Graphene XT Speed Pro|newspaper=Tennis.com|access-date=2016-10-15}}</ref>

As of 2015, there is one product available for commercial use: a graphene-infused printer powder.<ref>{{cite web |url=https://www.noble3dprinters.com/product/graphenite-graphene-infused-3d-printer-powder-30-lbs-499-95 |title=GRAPHENITE – GRAPHENE INFUSED 3D PRINTER POWDER – 30 Lbs – $499.95 |publisher=Noble3DPrinters |work=noble3dprinters.com |accessdate=16 July 2015 }}{{Dead link|date=January 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> Many other uses for graphene have been proposed or are under development, in areas including electronics, [[biological engineering]], [[filtration]], lightweight/strong [[composite materials]], [[photovoltaic]]s and [[energy storage]].<ref name="auto"/><ref>{{cite web |url=http://www.graphenea.com/pages/graphene-uses-applications |title=Graphene Uses & Applications |publisher=Graphenea |accessdate=13 April 2014}}</ref> Graphene is often produced as a powder and as a dispersion in a polymer matrix. This dispersion is supposedly suitable for advanced composites,<ref>{{cite journal |pmid=23405887 |pmc=3601907 |year=2013 |last1=Lalwani |first1=G |title=Two-dimensional nanostructure-reinforced biodegradable polymeric nanocomposites for bone tissue engineering |journal=Biomacromolecules |volume=14 |issue=3 |pages=900–9 |last2=Henslee |first2=A. M. |last3=Farshid |first3=B |last4=Lin |first4=L |last5=Kasper |first5=F. K. |last6=Qin |first6=Y. X. |last7=Mikos |first7=A. G. |last8=Sitharaman |first8=B |doi=10.1021/bm301995s}}</ref><ref>{{cite journal |first1=M.A. |last1=Rafiee |first2=J. |last2=Rafiee |first3=Z. |last3=Wang |first4=H. |last4=Song |first5=Z.Z. |last5=Yu |first6=N. |last6=Koratkar |s2cid=18266151 |title=Enhanced mechanical properties of nanocomposites at low graphene content |journal=ACS Nano |volume=3 |issue=12 |year=2009 |pages=3884–3890 |doi=10.1021/nn9010472|pmid=19957928 }}</ref> paints and coatings, lubricants, oils and functional fluids, capacitors and batteries, thermal management applications, display materials and packaging, solar cells, inks and 3D-printers' materials, and barriers and films.<ref>{{cite web |url=http://www.appliedgraphenematerials.com/products/graphene-dispersions/ |title=Applied Graphene Materials plc :: Graphene dispersions |work=appliedgraphenematerials.com}}</ref>

In 2016, researchers have been able to make a graphene film that can absorb 95% of light incident on it.<ref>{{cite web|url=http://www.sciencealert.com/this-nanometre-thick-graphene-film-is-the-most-light-absorbent-material-ever-created|title=This nanometre-thick graphene film is the most light-absorbent material ever created|first=Peter|last=Dockrill}}</ref> It is also getting cheaper; recently scientists at the University of Glasgow have produced graphene at a cost that is 100 times less than the previous methods.<ref>{{Cite web|url=https://www.sciencealert.com/researchers-just-made-graphene-100-times-more-cheaply-than-ever-before|title=Researchers Just Made Graphene 100 Times More Cheaply Than Ever Before|last=MacDonald|first=Fiona|date=2015-11-23|website=ScienceAlert|language=en-gb|url-status=live|archive-url=|archive-date=|access-date=2019-11-10}}</ref>

On August 2, 2016, [[Briggs Automotive Company|BAC]]'s new Mono model is said to be made out of graphene as a first of both a street-legal track car and a production car.<ref>{{Cite web |url=http://blog.dupontregistry.com/news/bac-debuts-first-ever-graphene-constructed-vehicle/ |title=BAC Debuts First Ever Graphene Constructed Vehicle |date=2016-08-02 |access-date=2016-08-04}}</ref><ref>{{Cite web|url=https://blog.dupontregistry.com/news/bac-debuts-first-ever-graphene-constructed-vehicle/|title=BAC Debuts First Ever Graphene Constructed Vehicle|last=|first=|date=2016-08-02|website=duPont Registry Daily|language=en-US|url-status=live|archive-url=|archive-date=|access-date=2019-11-10}}</ref>

In January 2018, graphene based spiral [[inductor]]s exploiting [[kinetic inductance]] at room temperature were first demonstrated at the [[University of California, Santa Barbara]], led by [[Kaustav Banerjee]]. These inductors were predicted to allow significant miniaturization in [[Radio frequency|radio-frequency]] [[integrated circuit]] applications.<ref>{{Cite journal | doi=10.1038/s41928-017-0010-z| title=On-chip intercalated-graphene inductors for next-generation radio frequency electronics| year=2018| last1=Kang| first1=Jiahao| last2=Matsumoto| first2=Yuji| last3=Li| first3=Xiang| last4=Jiang| first4=Junkai| last5=Xie| first5=Xuejun| last6=Kawamoto| first6=Keisuke| last7=Kenmoku| first7=Munehiro| last8=Chu| first8=Jae Hwan| last9=Liu| first9=Wei| last10=Mao| first10=Junfa| last11=Ueno| first11=Kazuyoshi| last12=Banerjee| first12=Kaustav| journal=Nature Electronics| volume=1| pages=46–51}}</ref><ref>{{Cite web|url=https://www.forbes.com/sites/startswithabang/2018/03/08/breakthrough-in-miniaturized-inductors-to-revolutionize-electronics/#55414a40779e|title=The Last Barrier to Ultra-Miniaturized Electronics is Broken, Thanks To A New Type Of Inductor|last=Siegel|first=E.|year=2018|website=Forbes.com|url-status=live|archive-url=|archive-date=|access-date=}}</ref><ref>{{Cite web|url=https://physicsworld.com/a/engineers-reinvent-the-inductor-after-two-centuries/|title=Engineers reinvent the inductor after two centuries|last=|first=|year=2018|website=physicsworld|url-status=live|archive-url=|archive-date=|access-date=}}</ref>

The potential of epitaxial graphene on SiC for metrology has been shown since 2010, displaying quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene. Over the years precisions of parts-per-trillion in the Hall resistance quantization and giant quantum Hall plateaus have been demonstrated. Developments in encapsulation and doping of epitaxial graphene have lead to the commercialisation of epitaxial graphene quantum resistance standards.<ref>{{cite journal |last1=Reiss |first1=T. |last2=Hjelt |first2=K. |last3=Ferrari |first3=A.C. |title=Graphene is on track to deliver on its promises |journal=Nature Nanotechnology |date=2019 |volume=14 |issue=907 |pages=907–910 |doi=10.1038/s41565-019-0557-0|pmid=31582830 |bibcode=2019NatNa..14..907R }}</ref>

==Health risks==
The toxicity of graphene has been extensively debated in the literature. The most comprehensive review on graphene toxicity published by Lalwani et al. exclusively summarizes the in vitro, in vivo, antimicrobial and environmental effects and highlights the various mechanisms of graphene toxicity.<ref>{{cite journal |pmid=27154267 |pmc=5039077 |year=2016 |last1=Lalwani |first1=Gaurav |title=Toxicology of graphene-based nanomaterials |journal=Advanced Drug Delivery Reviews |volume=105 |issue=Pt B |pages=109–144 |last2=D'Agati |first2=Michael |last3=Mahmud Khan |first3=Amit |last4=Sitharaman |first4=Balaji |doi=10.1016/j.addr.2016.04.028 |url= }}</ref>
Results show that the toxicity of graphene is dependent on several factors such as shape, size, purity, post-production processing steps, oxidative state, functional groups, dispersion state, synthesis methods, route and dose of administration, and exposure times.<ref>{{cite journal|pmc=7287048|year=2020|last1=Joshi |first1= Shubhi |title=Green synthesis of peptide functionalized reduced graphene oxide (rGO) nano bioconjugate with enhanced antibacterial activity|journal= Scientific Reports |volume=10 |issue=9441|pages=1–11 |last2=Siddiqui |first2=Ruby |last3=Sharma |first3=Pratibha |last4=Kumar |first4=Rajesh |last5=Verma |first5=Gaurav |last6=Saini |first6=Avneet|doi=10.1038/s41598-020-66230-3 |url= }}</ref>

Research at Stony Brook University showed that graphene [[nanoribbon]]s, graphene nanoplatelets and graphene nano–onions are non-toxic at concentrations up to 50&nbsp;μg/ml. These nanoparticles do not alter the differentiation of human bone marrow stem cells towards osteoblasts (bone) or adipocytes (fat) suggesting that at low doses graphene nanoparticles are safe for biomedical applications.<ref>{{cite journal |pmid=24674462 |pmc=3995421 |year=2014 |last1=Talukdar |first1=Y |title=The effects of graphene nanostructures on mesenchymal stem cells |journal=Biomaterials |volume=35 |issue=18 |pages=4863–77 |last2=Rashkow |first2=J. T. |last3=Lalwani |first3=G |last4=Kanakia |first4=S |last5=Sitharaman |first5=B |doi=10.1016/j.biomaterials.2014.02.054 |url= }}</ref> Research at Brown university found that 10&nbsp;μm few-layered graphene flakes are able to pierce cell membranes in solution. They were observed to enter initially via sharp and jagged points, allowing graphene to be internalized in the cell. The physiological effects of this remain uncertain, and this remains a relatively unexplored field.<ref>{{cite web |url=https://news.brown.edu/articles/2013/07/graphene |title=Jagged graphene edges can slice and dice cell membranes - News from Brown |work=brown.edu}}</ref><ref>{{Cite journal |doi=10.1073/pnas.1222276110 |pmid=23840061 |pmc=3725082 |title=Graphene microsheets enter cells through spontaneous membrane penetration at edge asperities and corner sites |journal=Proceedings of the National Academy of Sciences |volume=110 |issue=30 |pages=12295–12300 |year=2013 |last1=Li |first1=Y. |last2=Yuan |first2=H. |last3=von Dem Bussche |first3=A. |last4=Creighton |first4=M. |last5=Hurt |first5=R. H. |last6=Kane |first6=A. B. |last7=Gao |first7=H. |bibcode=2013PNAS..11012295L}}</ref>

==See also==
{{columns-list|
* [[Bilayer graphene]]
* [[Bismuth#Bismuthine and bismuthides|Bismuthide]]
* [[Borophene]]
* [[Cadmium arsenide]]
* [[Exfoliated graphite nano-platelets]]
* [[Germanene]]
* [[Graphene antenna]]
* [[Graphene applications as optical lenses]]
* [[Graphyne]]
* [[Metal-organic framework]]
* [[Molybdenum diselenide]]
* [[Molybdenum disulfide]]
* [[Nanoribbon]]
* [[Penta-graphene]]
* [[Phagraphene]]
* [[Plumbene]]
* [[Silicene]]
* [[Solid-state engine]]
* [[Stanene]]
* [[Two-dimensional polymers (2DP)|Two-dimensional polymers]]
}}

==References==

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<ref name=grima2014>{{cite journal |last1=Grima |first1=J. N. |last2=Winczewski |first2=S. |last3=Mizzi |first3=L. |last4=Grech |first4=M. C. |last5=Cauchi |first5=R. |last6=Gatt |first6=R. |last7=Attard |first7=D. |last8=Wojciechowski |first8=K.W. |last9=Rybicki |first9=J. |title=Tailoring Graphene to Achieve Negative Poisson's Ratio Properties |doi=10.1002/adma.201404106 |journal=Advanced Materials |year=2014 |volume=27 |issue=8 |pages=1455–1459 |pmid=25504060}}</ref>

<ref name=lixu2014>{{cite journal |last1=Li |first1=Xueming |last2=Lau |first2=Shu Ping |last3=Tang |first3=Libin |last4=Ji |first4=Rongbin |last5=Yang |first5=Peizhi |s2cid=23688312 |title=Sulphur Doping: A Facile Approach to Tune the Electronic Structure and Optical Properties of Graphene Quantum Dots |journal=Nanoscale |date=2014 |volume=6 |issue=10 |pages=5323–5328 |doi=10.1039/C4NR00693C |pmid=24699893 |bibcode=2014Nanos...6.5323L}}</ref>

<ref name=manch2014>{{cite web| author=<!--Staff writer(s); no by-line.--> |title=The Story of Graphene |url=http://www.graphene.manchester.ac.uk/explore/the-story-of-graphene|date=10 September 2014 |website=www.graphene.manchester.ac.uk |publisher=The University of Manchester |accessdate=9 October 2014 |quote="Following discussions with colleagues, Andre and Kostya adopted a method that researchers in surface science were using – using simple Sellotape to peel away layers of graphite to expose a clean surface for study under the microscope."}}</ref>

<ref name=mrmak2014>{{Cite web|last=Mrmak|first=Nebojsa|date=2014-11-28|title=Graphene properties (A Complete Reference)|url=http://www.graphene-battery.net/graphene-properties.htm|url-status=live|archive-url=|archive-date=|access-date=2019-11-10|website=Graphene-Battery.net}}</ref>

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<ref name=thej2014>{{cite news |publisher=The Journal.ie |title=Global breakthrough: Irish scientists discover how to mass produce 'wonder material' graphene |url=http://www.thejournal.ie/graphene-irish-researchers-major-breakdown-mass-production-1424843-Apr2014/ |date=20 April 2014 |accessdate=20 December 2014}}</ref>

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<ref name=zdet2015>Aristides D. Zdetsis and E. N. Economou (2015): "A pedestrian approach to the aromaticity of graphene and nanographene: Significance of Huckel’s (4n+2)π electron rule". ''Journal of Physical Chemistry - Series C'', volume 119, issue 29, pages 16991–17003. {{doi|10.1021/acs.jpcc.5b04311}}</ref>

<ref name=harris2018>Peter J. F. Harris (2018): "Transmission electron microscopy of carbon: A brief history".  ''C - Journal of Carbon Research'', volume 4, issue 1, article 4 (17 pages). {{doi|10.3390/c4010004}}</ref>

<ref name=dixit2019>{{cite journal |last1=Dixit |first1=Vaibhav A. |last2=Singh |first2=Yashita Y. |title=How much aromatic are naphthalene and graphene? |journal=Computational and Theoretical Chemistry |volume=1162 |pages=112504 |date=June 2019 |doi=10.1016/j.comptc.2019.112504}}</ref>

<ref name=prnews2019>{{cite news |title=Global Graphene Market Size is Expected to Reach $151.4 Million and Register a CAGR of 47.7% by 2021, Market Trends, Growth & Forecast - Valuates Report |url=https://www.prnewswire.com/news-releases/global-graphene-market-size-is-expected-to-reach-151-4-million-and-register-a-cagr-of-47-7-by-2021--market-trends-growth--forecast---valuates-report-300964539.html |accessdate=29 January 2020 |work=PR Newswire |publisher=Cision |date=25 November 2019}}</ref>

<ref name=cao2020>{{cite journal|last=Cao|first=K.|date=2020|title=Elastic straining of free-standing monolayer graphene|journal=Nature Communications|volume=11|issue=284|page=284|bibcode=2020NatCo..11..284C|doi=10.1038/s41467-019-14130-0|pmc=6962388|pmid=31941941}}</ref>

</references>

==External links==
{{commons category|Graphene}}
* [http://www.graphene.manchester.ac.uk/ Manchester's Revolutionary 2D Material] at ''[[The University of Manchester]]''
* [http://www.periodicvideos.com/videos/mv_graphene.htm Graphene] at ''[[The Periodic Table of Videos]]'' (University of Nottingham)
* [http://www.bbc.co.uk/news/science-environment-20975580 Graphene: Patent surge reveals global race]
* [https://www.cdc.gov/niosh/surveyreports/pdfs/356-12a.pdf 'Engineering Controls for Nano-scale Graphene Platelets During Manufacturing and Handling Processes' (PDF)]
* [https://nanohub.org/resources/723/download/2004.10.20-l21-ece453.pdf Band structure of graphene (PDF).]

{{Allotropes of carbon}}
{{emerging technologies|topics=yes|robotics=yes|manufacture=yes|materials=yes}}
{{Molecules detected in outer space}}

{{Authority control}}

[[Category:Graphene| ]]
[[Category:Aromatic compounds]]
[[Category:Emerging technologies]]
[[Category:Nanomaterials]]
[[Category:Quantum Lattice models]]
[[Category:Quantum phases]]
[[Category:Group IV semiconductors]]
[[Category:Superhard materials]]
[[Category:Monolayers]]
[[Category:Articles containing video clips]]
[[Category:21st-century inventions]]