# Graphene

Graphene is an atomic-scale honeycomb lattice made of carbon atoms.

Graphene is a 2-dimensional, crystaline allotrope of carbon. In graphene, carbon atoms are densely packed in a regular sp2-bonded atomic-scale chicken wire (hexagonal) pattern. Graphene can be described as a one-atom thick layer of graphite. It is the basic structural element of other allotropes, including graphite, charcoal, carbon nanotubes and fullerenes. It can also be considered as an indefinitely large aromatic molecule, the limiting case of the family of flat polycyclic aromatic hydrocarbons.

High-quality graphene is strong, light, nearly transparent and an excellent conductor of heat and electricity. Its interactions with other materials and with light and its inherently two-dimensional nature produce unique properties, such as the bipolar transistor effect, ballistic transport of charges and large quantum oscillations.

At the time of its isolation in 2004,1 researchers studying carbon nanotubes were already familiar with graphene's composition, structure and properties, which had been calculated decades earlier. The combination of familiarity, extraordinary properties, surprising ease of isolation and unexpectedly high quality of the obtained graphene enabled a rapid increase in graphene research. Andre Geim and Konstantin Novoselov at the University of Manchester won the Nobel Prize in Physics in 2010 "for groundbreaking experiments regarding the two-dimensional material graphene".2

## Definition

"Graphene" is a combination of graphite and the suffix -ene, named by Hanns-Peter Boehm,3 who described single-layer carbon foils in 1962.4

The term graphene first appeared in 19875 to describe single sheets of graphite as one of the constituents of graphite intercalation compounds (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of carbon nanotubes,6 as well as for epitaxial graphene7 and polycyclic aromatic hydrocarbons.8

The IUPAC compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene... it is incorrect to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed."9

Graphene can be considered an "infinite alternant" (only six-member carbon ring) polycyclic aromatic hydrocarbon (PAH). The largest known isolated PAH molecule consists of 222 atoms and is 10 benzene rings across.10 It has proven difficult to synthesize even slightly bigger molecules, and they still remain "a dream of many organic and polymer chemists".11

A definition of "isolated or free-standing graphene" was proposed: "graphene is a single atomic plane of graphite, which  – and this is essential – is sufficiently isolated from its environment to be considered free-standing."12 This definition is narrower than the definition given above and refers to cleaved, transferred and suspended graphene monolayers.citation needed Other forms of graphene, such as graphene grown on various metals, can become free-standing if, for example, suspended or transferred to silicon dioxide (SiO
2
) or silicon carbide (after its passivation with hydrogen).13

## History

In 1859 Benjamin Collins Brodie was aware of the highly lamellar structure of thermally reduced graphite oxide.14

The structure of graphite was solved in 1916.15 by the related method of powder diffraction,1617 It was studied in detail by V. Kohlschütter and P. Haenni in 1918, who also described the properties of graphite oxide paper.18 Its structure was determined from single-crystal diffraction in 1924.1920

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 by Gordon Walter Semenoff and David P. DeVincenzo and Eugene J. Mele.21 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.222324

The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948.25 Later, single graphene layers were also observed directly by electron microscopy.26 Before 2004 intercalated graphite compounds were studied under a transmission electron microscope (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962.2728

Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials.29 This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp2-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate to the epitaxial graphene, and, in some cases, hybridization between the d-orbitals of the substrate atoms and π orbitals of graphene, which significantly alters the electronic structure of epitaxial graphene.

Single layers of graphite were also observed by transmission electron microscopy within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990,30 but nothing thinner than 50 to 100 layers was produced before 2004.

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.

Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.31 Old papers were unearthed27 in which researchers tried to isolate graphene starting with intercalated compounds. These papers reported the observation of very thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the earlier observations was sufficient to "spark the graphene gold rush", which awaited macroscopic samples of extracted atomic planes.

One of the very first patents pertaining to the production of graphene was filed in October, 2002 (US Pat. 7071258).32 Entitled, "Nano-scaled Graphene Plates", this patent detailed one of the very first large scale graphene production processes. Two years later, in 2004 Andre Geim and Kostya Novoselov at University of Manchester extracted single-atom-thick crystallites from bulk graphite.33 They pulled graphene layers from graphite and transferred them onto thin SiO
2
on a silicon wafer in a process called either micromechanical cleavage or the Scotch tape technique. The SiO
2
electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the SiO
2
could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. They may not have been the first to use this technique—patent 6667100 US , filed in 2002, describes how to process commercially available flexible expanded graphite to achieve a graphite thickness of 0.01 thousandth of an inch. The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast.

The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene,2224 which provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions. The effect was reported soon after by Philip Kim and Yuanbo Zhang in 2005. These experiments started after the researchers observed colleagues who were looking for the quantum Hall effect34 and Dirac fermions35 in bulk graphite.

Even though graphene on nickel and on silicon carbide have both existed in the laboratory for decades, graphene mechanically exfoliated on SiO
2
provided the first proof of the Dirac fermion nature of electrons.citation needed

Andre Geim and Konstantin Novoselov, 2010

Geim and Novoselev received several awards for their pioneering research on graphene, notably the 2010 Nobel Prize in Physics.36

## Properties

### Structure

The atomic structure of isolated, single-layer graphene was studied by transmission electron microscopy (TEM) on sheets of graphene suspended between bars of a metallic grid.26 Electron diffraction patterns showed the expected honeycomb lattice. Suspended graphene also showed "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,313738 or may originate from the ubiquitous dirt seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene on SiO
2
substrates are available3940 via scanning tunneling microscopy. Photoresist residue, which must be removed to obtain atomic-resolution images, may be the "adsorbates" observed in TEM images, and may explain the observed rippling. Rippling on SiO
2
is caused by conformation of graphene to the underlying SiO
2
, and is not intrinsic.39

Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.41 However, unlayered graphene with only (hk0) rings has been found in the core of presolar graphite onions.42 TEM studies show faceting at defects in flat graphene sheets43 and suggest a role for two-dimensional crystallization from a melt.

Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as hydrocarbons. Bombarded with pure carbon atoms, the atoms perfectly align into hexagons, completely filling the holes.4445

### Chemical

Graphene is the only form of carbon (and generally all solid materials) in which each single atom is in exposure for chemical reaction from two sides (due to the 2D structure). It is known that carbon atoms at the edge of graphene sheets have special chemical reactivity, and graphene has the highest ratio of edgy carbons (in comparison with similar materials such as carbon nanotubes). In addition, various types of defects within the sheet, which are very common, increase the chemical reactivity.46 The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below 260°C 47 and the graphene burns at very low temperature (e.g., 350 °C).48 In fact, graphene is chemically the most reactive form of carbon, owing to the lateral availability of carbon atoms. Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. But, determination of structures of graphene with oxygen-49 and nitrogen-50 containing functional groups is a difficult task unless the structures are well controlled.

In 2013, Stanford University physicists reported that sheets of Graphene one atom thick are a hundred times more chemically reactive than thicker sheets.51

### Physical

The carbon–carbon bond length in graphene is about 0.142 nanometers.52 Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm.

### Electronic

GNR band structure for zig-zag orientation. Tightbinding calculations show that zigzag orientation is always metallic.
GNR band structure for armchair orientation. Tightbinding calculations show that armchair orientation can be semiconducting or metallic depending on width (chirality).

Graphene differs from most three-dimensional materials. Intrinsic graphene is a semi-metal or zero-gap semiconductor. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. The energy-momentum relation (dispersion relation) is linear for low energies near the six corners of the two-dimensional hexagonal Brillouin zone, leading to zero effective mass for electrons and holes.53 Due to this linear (or “conical") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like relativistic particles described by the Dirac equation for spin-1/2 particles.5455 Hence, the electrons and holes are called Dirac fermions and the six corners of the Brillouin zone are called the Dirac points.54 The equation describing the electrons' linear dispersion relation is $E = \hbar v_F\sqrt{k_x^2+k_y^2}$; where the Fermi velocity vF ~ 106 m/s, and the wavevector k is measured from the Dirac points (the zero of energy is chosen here to coincide with the Dirac points).55

Electrical resistance in 40-nanometer-wide nanoribbons of epitaxially-applied graphene changes in discrete steps following quantum mechanical principles. Graphene nanoribbons can act more like optical waveguides or quantum dots, allowing electrons to flow smoothly along the material's edges. In conductors such as copper, resistance increases in proportion to the length as electrons encounter more and more impurities while moving through the conductor. Electrons travel ballistically, similar to those observed in cylindrical carbon nanotubes, exceeding theoretical conductance predictions for graphene by a factor of 10. Electrons in the nanoribbons can move tens or hundreds of microns without scattering.5657

The measured graphene nanoribbons were approximately 40 nanometers wide that had been grown on the edges of three-dimensional structures etched into silicon carbide wafers. When the wafers are heated to approximately 1,000 °C (1,830 °F), silicon is preferentially driven off along the edges, forming graphene nanoribbons whose structure is determined by the pattern of the three-dimensional surface.56

The nanoribbons have perfectly smooth edges, annealed by the fabrication process. Electrons on the edge flow more like photons in optical fiber, helping them avoid scattering. Ballistic conductance extended for up to 16 microns. Electron mobility measurements surpassing one million correspond to a sheet resistance of one ohm per square— two orders of magnitude lower than what is observed in two-dimensional graphene and one tenth of theoretical predictions.56

Transport is dominated by two modes. One is ballistic and temperature independent; while the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres.56

Theoretical explanations of the phenomenon are incomplete, although they may produce a new type of electronic transport similar to what is observed in superconductors.56

### "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. Both states exist at exactly zero energy. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hBN 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.58

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.58

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 dots, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against backscattering and could carry currents without dissipation.58

#### Electron transport

Experimental results from transport measurements show that graphene has a remarkably high electron mobility at room temperature, with reported values in excess of 15,000 cm2·V−1·s−1.31 Additionally, the symmetry of the experimentally measured conductance indicates that hole and electron mobilities should be nearly the same.53 The mobility is nearly independent of temperature between 10 K and 100 K,225960 which implies that the dominant scattering mechanism is defect scattering. Scattering by the acoustic phonons of graphene intrinsically limits room temperature mobility to 200,000 cm2·V−1·s−1 at a carrier density of 1012 cm−2.6061 The corresponding resistivity of the graphene sheet would be 10−6 Ω·cm. This is less than the resistivity of silver, the lowest known at room temperature.62 However, for graphene on SiO
2
substrates, scattering of electrons by optical phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons. This limits mobility to 40,000 cm2·V−1·s−1.60

Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of $4e^2/h$. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the SiO
2
substrate may lead to local puddles of carriers that allow conduction.53 Several theories suggest that the minimum conductivity should be $4e^2/{(\pi}h)$; however, most measurements are of order $4e^2/h$ or greater31 and depend on impurity concentration.63

Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum.6364 Even for dopant concentrations in excess of 1012 cm2 carrier mobility exhibits no observable change.64 Graphene doped with potassium in ultra-high vacuum at low temperature can reduce mobility 20-fold.6365 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 quantum66) is thought to occur. It may therefore be a suitable material for constructing quantum computers67 using anyonic circuits.68

### Optical

Photograph of graphene in transmitted light. This one-atom-thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light.

Graphene's unique optical properties produce an unexpectedly high opacity for an atomic monolayer in vacuum, absorbing πα ≈ 2.3% of white light, where α is the fine-structure constant.69 This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole conical bands meeting each other at the Dirac point... [which] is qualitatively different from more common quadratic massive bands".70 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.71

Graphene's band gap can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by applying voltage to a dual-gate bilayer graphene field-effect transistor (FET) at room temperature.72 The optical response of graphene nanoribbons is tunable into the terahertz regime by an applied magnetic field.73 Graphene/graphene oxide systems exhibit electrochromic behavior, allowing tuning of both linear and ultrafast optical properties.74

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 633 nm He-Ne laser as the light source.75

#### 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 lasers, 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.7476 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 microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.77

#### 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 non-linear Kerr coefficient of 10−7 cm2·W−1, almost nine orders of magnitude larger than that of bulk dielectrics.78 This suggests that graphene may be a nonlinear Kerr medium, paving the way for graphene-based nonlinear Kerr photonics such as a soliton.

### 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.79 With GW calculation, the properties of graphene-based materials are accurately investigated, including graphene,80 graphene nanoribbons,81 edge and surface functionalized armchair graphene nanoribbons,82 hydrogen saturated armchair graphene nanoribbons,83 Josephson effect in graphene SNS junctions with single localized defect84 and scaling properties in armchair graphene nanoribbons.85

### Thermal

#### Stability

Ab initio calculations show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm (“graphene is the least stable structure until about 6000 atoms”) and becomes the most stable fullerene (as within graphite) only for molecules larger than 24,000 atoms.86

#### Conductivity

The near-room temperature thermal conductivity of graphene was measured to be between (4.84±0.44) × 103 to (5.30±0.48) × 103 W·m−1·K−1. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamonds. The isotopic composition, the ratio of 12C to 13C, has a significant impact on thermal conductivity, where isotopically pure 12C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.87 It can be shown by using the Wiedemann–Franz law, that the thermal conduction is phonon-dominated.88 However, for a gated graphene strip, an applied gate bias causing a Fermi energy shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.8990

Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has basal planethermal conductivity of over a 1000 W·m−1·K−1 (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.91 In addition, the ballistic thermal conductance of a graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.92

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 T2 dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T1.5 contribution of the out of plane mode.92 Some graphene phonon bands display negative Grüneisen parameters.93 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 transversal 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 Lifshitz in 1952.94

### Mechanical

The flat graphene sheet is unstable with respect to scrolling i.e. bending into a cylindrical shape, which is its lower-energy state.95

As of 2009, graphene appeared to be one of the strongest materials known with a breaking strength over 100 times greater than a hypothetical steel film of the same (thin) thickness,96 with a Young's modulus (stiffness) of 1 TPa (150,000,000 psi).97 The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a 4 kg cat but would weigh only as much as one of the cat's whiskers, at 0.77 mg (about 0.001% of the weight of 1 m2 of paper).96

However, the process of separating it from graphite, where it occurs naturally, requires technological development to be economical enough to be used in industrial processes.9899

The spring constant of suspended graphene sheets has been measured using an atomic force microscope (AFM). Graphene sheets, held together by van der Waals forces, were suspended over SiO
2
cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was 0.5 TPa, which differs from that of bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for NEMS applications such as pressure sensors and resonators.100

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,26 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.313738101

### 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 moments in carbon (as well as a weak hyperfine interaction). Electrical spin current injection and detection has been demonstrated up to room temperature.102103104 Spin coherence length above 1 micrometre at room temperature was observed,102 and control of the spin current polarity with an electrical gate was observed at low temperature.103

### Anomalous quantum Hall effect

The quantum Hall effect is relevant for accurate measuring of electrical quantities, and in 1985 Klaus von Klitzing received the Nobel prize for its discovery. The effect concerns the dependence of a transverse conductivity on a magnetic field, which is perpendicular to a current-carrying stripe. Usually the phenomenon, the quantization of the so-called Hall conductivity $\sigma_{xy}$ at integer multiples (the "Landau level") of the basic quantity $e^2/h$ (where e is the elementary electric charge and h is Planck's constant) can be observed only in very clean silicon or gallium arsenide solids at very low temperatures around 3 K and very high magnetic fields.

In contrast graphene shows the quantum Hall effect just in the presence of a magnetic field and just 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 $\sigma_{xy} = \pm {4\cdot\left(N + 1/2 \right)e^2}/h$, where N is the Landau level and the double valley and double spin degeneracies give the factor of 4.31 Moreover, in graphene these anomalies are present at room temperature, i.e. at roughly 20 °C.22 This anomalous 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,54 leading to the "+1/2" in the Hall conductivity.23 Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. $\sigma_{xy} = \pm {4\cdot N\cdot e^2}/h$). In the second anomaly, the first plateau at N = 0 is absent, indicating that bilayer graphene stays metallic at the neutrality point.31

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 oscillations, which show a phase shift of π, known as Berry’s phase.2253 Berry’s phase arises due to the zero effective carrier mass near the Dirac points.24 Study of the temperature dependence of graphene's Shubnikov–de Haas oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from the E–k relation.22

Graphene samples prepared on nickel films, and on both the silicon face and carbon face of silicon carbide, show the anomalous quantum Hall effect directly in electrical measurements.105106107108109110 Graphitic layers on the carbon face of silicon carbide show a clear Dirac spectrum in angle-resolved photoemission experiments, and the anomalous quantum Hall effect is observed in cyclotron resonance and tunneling experiments.111

#### Strong magnetic fields

Graphene's quantum Hall effect in magnetic fields above 10 Teslas or so reveals additional interesting features. Additional plateaus of the Hall conductivity at $\sigma_{xy} = \nu e^2/h$ with $\nu = 0,\pm {1},\pm {4}$ are observed.112 Also, the observation of a plateau at $\nu = 3$113 and the fractional quantum Hall effect at $\nu = 1/3$ were reported.113114

These observations with $\nu = 0,\pm 1,\pm 3, \pm 4$ indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the magnetic catalysis of symmetry breaking is responsible for lifting the degeneracy.citation needed

## Forms

### Nanostripes

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.115)

### Graphene 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.116 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.117 Graphene oxide flakes in polymers display enhanced photo-conducting properties.118 Graphene-based membranes are impermeable to all gases and liquids (vacuum-tight). However, water evaporates through them as quickly as if the membrane was not present.119

### Chemical modification

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 laboratory120 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 5.3 angstrom thickness) is soluble in tetrahydrofuran, tetrachloromethane and dichloroethane.

Refluxing single-layer graphene oxide (SLGO) in solvents 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 dependant 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%.

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 titrations 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 carbodiimides leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (ca. 3–5% conversion of the intermediate to the final amide).121 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.122

Full hydrogenation from both sides of graphene sheet results in graphane, but partial hydrogenation leads to hydrogenated graphene.123 Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to fluorographene (graphene fluoride), while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene.

### Casimir effect and dispersion

The Casimir effect is an interaction between any 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 surfaces of the interacting bodies. Since the interaction of graphene with an electromagnetic field is surprisingly strong for a one-atom-thick material, the Casimir effect is of growing interest.124125

The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.126

### Bilayer graphene

Bilayer graphene displays the anomalous quantum Hall effect, a tunable band gap127 and potential for excitonic condensation128 –making them promising candidates for optoelectronic and nanoelectronic applications. Bilayer graphene typically can be found either in 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. Stacking order and orientation govern the optical and electronic properties of bilayer graphene.

One way to synthesize bilayer graphene is via chemical vapor deposition, and can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.129

### 3D graphene

In 2013, a three-dimensional honeycomb of hexagonally arranged carbon was termed 3D graphene, although self-supporting 3D graphene has not yet been produced.130

## Production techniques

True isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle. However, other routes to 2d materials exist:

Fundamental forces place seemingly insurmountable barriers in the way of creating [2D crystals]... The nascent 2D crystallites try to minimize their surface energy and inevitably morph into one of the rich variety of stable 3D structures that occur in soot.

But there is a way around the problem. Interactions with 3D structures stabilize 2D crystals during growth. So one can make 2D crystals sandwiched between or placed on top of the atomic planes of a bulk crystal. In that respect, graphene already exists within graphite... One can then hope to fool Nature and extract single-atom-thick crystallites at a low enough temperature that they remain in the quenched state prescribed by the original higher-temperature 3D growth.131

Graphene planes become better separated in intercalated graphite compounds.

Graphene fragments are produced (along with other debris) whenever graphite is abraded, such as when drawing with a pencil.30

In 2011 the Institute of Electronic Materials Technology and Department of Physics at Warsaw University announced Sicilicon-based epitaxy technology for producing large pieces of graphene with the best quality to date.132

### Mechanical exfoliation

This involves splitting single layers of graphene from multi-layered graphite. Achieving single layers typically requires multiple exfoliation steps, each producing a slice with fewer layers, until only one remains. Geim and Novosolev used adhesive tape to split the layers.

After exfoliation the flakes are deposited on a silicon wafer using "dry deposition". Individual atomic planes can be viewed with an optical microscope. Crystallites larger than 1 mm and visible to the naked eye can be obtained with the technique. It is often referred to as a "scotch tape" or "drawing" method. The latter name appeared because the dry deposition resembles drawing with a piece of graphite.131

### Epitaxy

Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by Van der Waals forces) to retain the two dimensional electronic band structure of isolated graphene.133134 An example of weakly coupled epitaxial graphene is the one grown on SiC.33

Graphene monolayers grown on SiC and Ir are weakly coupled to these substrates (how weakly remains debated) and the graphene–substrate interaction can be further passivated.13

#### Silicon carbide

Heating silicon carbide (SiC) to high temperatures (>1100 °C) under low pressures (~10−6 torr) reduces it to graphene.135 This process produces epitaxial graphene with dimensions dependent upon the size of the wafer. The face of the SiC used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the resulting graphene.

The electronic band-structure (so-called Dirac cone structure) was first visualized in this material.136137138 Weak anti-localization is observed in this material, but not in exfoliated graphene produced by the pencil-trace method.139 Large, temperature-independent mobilities have been observed, approaching those in exfoliated graphene placed on silicon oxide, but lower than mobilities in suspended graphene produced by the drawing method. Even without transfer, graphene on SiC exhibits massless Dirac fermions.105106107108109110

The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single layer,140 in other cases the properties are affected,136137 as they are in bulk graphite. This effect is well understood theoretically and is related to the symmetry of the interlayer interactions.140

Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The band gap can be tuned by laser irradiation.141

#### Metal substrates

The atomic structure of a metal substrate can seed the growth of graphene. Graphene grown on ruthenium does not typically produce uniform layer thickness. Bonding between the bottom graphene layer and the substrate may affect layer properties.142

Graphene grown on iridium is very weakly bonded, uniform in thickness and can be highly ordered. As on many other substrates, graphene on iridium is slightly rippled. Due to the long-range order of these ripples, minigaps in the electronic band-structure (Dirac cone) become visible.143 High-quality sheets of few-layer graphene exceeding 1 cm2 (0.2 sq in) in area have been synthesized via chemical vapor deposition on thin nickel films with methane as a carbon source. These sheets have been successfully transferred to various substrates.105144145

An improvement of this technique employs copper foil; at very low pressure, the growth of graphene automatically stops after a single graphene layer forms. Arbitrarily large films can be created.144146 The single layer growth is also due to low concentration of carbon in methane. Larger hydrocarbons such as ethane and propane produce bilayer graphene.147 Atmospheric pressure CVD growth produces multilayer graphene on copper (similar to that grown on nickel films).148 Graphene has been demonstrated at temperatures compatible with conventional CMOS processing, using a nickel-based alloy with gold as catalyst.149

### Reduction of graphite oxide

Graphite oxide reduction was probably the first method of graphene synthesis. P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.150 Geim acknowledged Boehm's contribution.151 Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide monolayer films, e.g. by hydrazine, annealing in argon/hydrogen, was reported to yield graphene films. However, the quality is lower compared to scotch-tape graphene, due to incomplete removal of functional groups. Furthermore, the oxidation protocol introduces permanent defects due to over-oxidation. Recently, the oxidation protocol was enhanced to yield graphene oxide with an almost intact carbon framework that allows highly efficient removal of functional groups. The measured charge carrier mobility exceeded 1,000 centimetres (393.70 in)/Vs.152 Spectroscopic analysis of reduced graphene oxide has been conducted.49153

Applying a layer of graphite oxide film to a DVD and burning it in a DVD writer produced a thin graphene film with high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram), and was highly resistant and malleable.154

### Metal-carbon melts

This process dissolves carbon atoms inside a transition metal melt at a certain temperature and then precipitates the dissolved carbon at lower temperatures as single layer graphene (SLG).155

The metal is first melted in contact with a carbon source, possibly a graphite crucible inside which the melt is carried out or graphite powder or chunks that are placed in the melt. Keeping the melt in contact with the carbon at a specific temperature dissolves the carbon atoms, saturating the melt based on the binary phase diagram of metal-carbon. Upon lowering the temperature, carbon's solubility decreases and the excess carbon precipitates atop the melt. The floating layer can be either skimmed or frozen for later removal. Using different morphology, including thick graphite, few layer graphene (FLG) and SLG were observed on metal substrate. Raman spectroscopy proved that SLG had grown on nickel substrate. The SLG Raman spectrum featured no D and D′ band, indicating its pristine nature. Among transition metals, nickel provides the best substrate for growing SLG. Since nickel is not Raman active, direct Raman spectroscopy of graphene layers on top of the nickel is achievable.155

### Sodium ethoxide pyrolysis

Gram-quantities of graphene were produced by the reduction of ethanol by sodium metal, followed by pyrolysis of the ethoxide product and washing with water to remove sodium salts.156

### Nanotube slicing

Graphene can be created by cutting open carbon nanotubes.157 In one such method multi-walled carbon nanotubes are cut open in solution by action of potassium permanganate and sulfuric acid.158 In another method graphene nanoribbons were produced by plasma etching of nanotubes partly embedded in a polymer film.159

### Solvent exfoliation

Dispersing graphite in a proper liquid medium can produce graphene by sonication. Non-exfoliated graphite is separated from graphene by centrifugation,160 producing graphene concentrations initially up to 0.01 mg/ml in N-methylpyrrolidone (NMP) and later to 2.1 mg/ml in NMP,.161 Using a suitable ionic liquid as the dispersing liquid medium for graphite exfoliation162 produced concentrations of 5.33 mg/ml. The concentration of graphene sheets produced by this method is very low because there is nothing preventing the sheets from restacking due to the van der Waals forces pulling them back together. the maximum concentrations achieved are the points at which the van der Waals forces overcome the interactive forces between the graphene sheets and the solvent molecules.

### Surfactant-aided exfoliation

Similar to solvent exfoliation, graphite is sonicated in a suitable solvent. In this case, however, surfactant molecules are added which prevent the restacking of the graphene sheets by adsorbing to the surface of the graphene. The concentration of graphene achieved by this method is higher than solvent exfoliation, but the removal of the surfactant molecules is often necessary and usually requires chemical treatments.

### Interface trapping

Macro-scale graphene films can be created by sonicating graphite while at the interface of two immiscible liquids, most notably heptane and water. The graphene sheets are exfoliated because of the sonication and then adsorbed to the high energy interface between the heptane and the water, where they are kept from restacking. The force holding the graphene at the interface is very strong, withstanding forces in excess of 300,000 g. The solvents may then be evaporated, leaving behind the graphene film. Films created using the interface trapping method are very transparent (up to ~95 %T) and conductive.163

### Carbon dioxide reduction

A highly exothermic reaction combusts magnesium in an oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including graphene and fullerenes. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The products of this reaction are carbon and magnesium oxide. US patent 8377408  was issued for this process.164

## Potential applications

Potential applications include lightweight, thin, flexible, yet durable display screens, electric circuits, and solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials.165

In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample with the area of the cross section of a human hair costing more than $1,000 as of April 2008 (about$100,000,000/cm2).30 Since then, exfoliation procedures have been scaled up, and now companies sell graphene in large quantities.166 The price of epitaxial graphene on SiC is dominated by the substrate price, which was approximately 100/cm2 as of 2009. Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using chemical vapour deposition (CVD) on thin nickel layers, which triggered research on practical applications,167 with wafer sizes up to 30 inches (760 mm) reported.144 In 2013, the European Union made a €1 billion grant to be used for research into potential graphene applications.168 In 2013 the Graphene Flagship consortium formed, including Chalmers University of Technology and seven other European universities and research centers, along with Nokia.169 Nokia has also been working on graphene technology for several years.170 ### Medicine Graphene is reported to have enhanced PCR by increasing the yield of DNA product.171 Experiments revealed that graphene's thermal conductivity could be the main factor behind this result. Graphene yields DNA product equivalent to positive control with up to 65% reduction in PCR cycles. ### Integrated circuits For integrated circuits, graphene has a high carrier mobility, as well as low noise, allowing it to be used as the channel in a field-effect transistor. Single sheets of graphene are hard to produce and even harder to make on an appropriate substrate.172 In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene.173 IBM announced in December 2008 that they had fabricated and characterized graphene transistors operating at GHz frequencies.174 In May 2009, an n-type transistor was announced meaning that both n and p-type graphene transistors had been created.175176 A functional graphene integrated circuit was demonstrated – a complementary inverter consisting of one p- and one n-type graphene transistor.177 However, this inverter suffered from a very low voltage gain. According to a January 2010 report,178 graphene was epitaxially grown on SiC in a quantity and with quality suitable for mass production of integrated circuits. At high temperatures, the quantum Hall effect could be measured in these samples. IBM built 'processors' using 100 GHz transistors on 2-inch (51 mm) graphene sheets.179 In June 2011, IBM researchers announced that they had succeeded in creating the first graphene-based integrated circuit, a broadband radio mixer.180 The circuit handled frequencies up to 10 GHz. Its performance was unaffected by temperatures up to 127 C. In June 2013 an 8 transistor 1.28 GHz ring oscillator circuit was described.181 #### Transistors Graphene exhibits a pronounced response to perpendicular external electric fields, potentially forming field-effect transistors (FET). A 2004 paper documented FETs with an on-off ratio of ~30 at room temperature.citation needed A 2006 paper announced an all-graphene planar FET with side gates.182 Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on–off ratio of <2) was demonstrated in 2007.183 Graphene nanoribbons may prove generally capable of replacing silicon as a semiconductor.184 US patent 7015142 for graphene-based electronics was issued in 2006. In 2008, researchers at MIT Lincoln Lab produced hundreds of transistors on a single chip185 and in 2009, very high frequency transistors were produced at Hughes Research Laboratories.186 A 2008 paper demonstrated a switching effect based on a reversible chemical modification of the graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible switches could potentially be employed in nonvolatile memories.187 In 2009, researchers demonstrated four different types of logic gates, each composed of a single graphene transistor.188 Practical uses for these circuits are limited by the very small voltage gain they exhibit. Typically, the amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of these circuits operated at frequencies higher than 25 kHz. In the same year, tight-binding numerical simulations189 demonstrated that the band-gap induced in graphene bilayer field effect transistors is not sufficiently large for high-performance transistors for digital applications, but can be sufficient for ultra-low voltage applications, when exploiting a tunnel-FET architecture.190 In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal gate length. The 240 nm devices were made with conventional silicon-manufacturing equipment.191192193 In November 2011, researchers used 3d printing (additive manufacturing) as a method for fabricating graphene devices.194 In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band frequency selectivity ranging from the THz to IR region (0.76-33THz)195 A separate group created a terahertz-speed transistor with bistable characteristics, which means that the device can spontaneously switch between two electronic states. The device consists of two layers of graphene separated by an insulating layer of boron nitride a few atomic layers thick. Electrons move through this barrier by quantum tunneling. These new transistors exhibit “negative differential conductance,” whereby the same electrical current flows at two different applied voltages.196 Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. The negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance — observed under certain biasing schemes — is an intrinsic property of graphene resulting from its symmetric band structure. The results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.197 In 2013 researchers reported the creation of transistors printed on flexible plastic that operate at 25-gigahertz, sufficient for communications circuits and that can be fabricated at scale. The researchers first fabricate the non-graphene-containing structures—the electrodes and gates—on plastic sheets. Separately, they grow large graphene sheets on metal, then peel it off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices work after being soaked in water, and are flexible enough to be folded.198 ### Redox Graphene oxide can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in switching between partially reduced graphene oxide and graphene, a process that modifies the electronic and optical properties. Oxidation and reduction are related to resistive switching.199 ### Transparent conducting electrodes Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, required for such applications as touchscreens, liquid crystal displays, organic photovoltaic cells, and organic light-emitting diodes. In particular, graphene's mechanical strength and flexibility are advantageous compared to indium tin oxide, which is brittle. Graphene films may be deposited from solution over large areas.200201 Large-area, continuous, transparent and highly conducting few-layered graphene ﬁlms were produced by chemical vapor deposition and used as anodes for application in photovoltaic devices. A power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control device based on indium tin oxide.202 Organic light-emitting diodes (OLEDs) with graphene anodes have been demonstrated.203 The electronic and optical performance of graphene-based devices are similar to devices made with indium tin oxide. A carbon-based device called a light-emitting electrochemical cell (LEC) was demonstrated with chemically-derived graphene as the cathode and the conductive polymer PEDOT as the anode.204 Unlike its predecessors, this device contains only carbon-based electrodes, with no metal. ### Ethanol distillation Graphene oxide membranes allow water vapor to pass through, but are impermeable to other liquids and gases.119 This phenomenon has been used for further distilling of vodka to higher alcohol concentrations, in a room-temperature laboratory, without the application of heat or vacuum as used in traditional distillation methods.205 Further development and commercialization of such membranes could revolutionize the economics of biofuel production and the alcoholic beverage industry. ### Desalination Research suggests that graphene filters could outperform other techniques of desalination by a significant margin.206 ### Solar cells Graphene has a unique combination of high electrical conductivity and optical transparency, which make it a candidate for use in solar cells. A single sheet of graphene is a zero-bandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for applications requiring a transparent conductor. Graphene can be assembled into a film electrode with low roughness. However, graphene films produced via solution processing contain lattice defects and grain boundaries that act as recombination centers and decrease the material's electrical conductivity. Thus, these films must be made thicker than one atomic layer to obtain useful sheet resistances. This added resistance can be combatted by incorporating conductive filler materials, such as a silica matrix. Reduced graphene film's electrical conductivity can be improved by attaching large aromatic molecules such as pyrene-1-sulfonic acid sodium salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic acid (PDI). These molecules, under high temperatures, facilitate better π-conjugation of the graphene basal plane. Graphene films have high transparency in the visible and near-infrared regions and are chemically and thermally stable.207 For graphene to be used in commercial solar cells, large-scale production are required. However, no scalable process for producing graphene is available, including the peeling of pyrolytic graphene or thermal decomposition of silicon carbide.207 Graphene's high charge mobilities recommend it for use as a charge collector and transporter in photovoltaics (PV). Using graphene as a photoactive material requires its bandgap to be 1.4-1.9eV. In 2010, single cell efficiencies of nanostructured graphene-based PVs of over 12% were achieved. According to P. Mukhopadhyay and R. K. Gupta organic photovoltaics could be "devices in which semiconducting graphene is used as the photoactive material and metallic graphene is used as the conductive electrodes".207 In 2013 In 2012, researchers from the University of Florida reported efficiency of 8.6% for a prototype cell consisting of a wafer of silicon coated with a layer of graphene doped with trifluoromethanesulfonyl-amide (TFSA). In 2013 another team claimed to have reached 15.6% percent using a combination of titanium oxide and graphene as a charge collector and perovskite as a sunlight absorber. The device is manufacturable at temperatures under 150 °C (302 °F) using solution-based deposition. This lowers production costs and offers the potential using flexible plastics.208209 Large scale production of highly transparent graphene films by chemical vapor deposition was achieved in 2008. In this process, ultra-thin graphene sheets are created by first depositing carbon atoms in the form of graphene films on a nickel plate from methane gas. A protective layer of thermoplastic is laid over the graphene layer and the nickel underneath is dissolved in an acid bath. The final step is to attach the plastic-protected graphene to a flexible polymer sheet, which can then be incorporated into an OPV cell. Graphene/polymer sheets range in size up to 150 square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be possible to run printing presses covering extensive areas with inexpensive solar cells, much like newspaper presses print newspapers (roll-to-roll).210 Silicon generates only one current-driving electron for each photon it absorbs, while graphene can produce multiple electrons. Solar cells made with graphene could offer 60% conversion efficiency – double the widely-accepted maximum efficiency of silicon cells.211 ### Single-molecule gas detection Theoretically graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect adsorbed molecules. However, similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules cannot be readily adsorbed onto graphene surfaces, so intrinsically graphene is insensitive.212 The sensitivity of graphene chemical gas sensors can be dramatically enhanced by functionalization, for example, coating the film with a thin layer of certain polymers. The thin polymer layer acts like a concentrator that absorbs gaseous molecules. The molecule absorption introduces a local change in electrical resistance of graphene sensors. While this effect occurs in other materials, graphene is superior due to its high electrical conductivity (even when few carriers are present) and low noise, which makes this change in resistance detectable.64 ### Quantum dots Graphene quantum dots (GQDs) keep all dimensions less than 10 nm. Their size and edge crystallography govern their electrical, magnetic, optical and chemical properties. GQDs can be produced via graphite nanotomy213 or via bottom-up, solution-based routes (Diels-Alder, cyclotrimerization and/or cyclodehydrogenation reactions).214 GQDs with controlled structure can be incorporated into applications in electronics, optoelectronics and electromagnetics. Quantum confinement can be created by changing the width of graphene nanoribbons (GNRs) at selected points along the ribbon.173215 ### Frequency multiplier In 2009, researchers built experimental graphene frequency multipliers that take an incoming signal of a certain frequency and output a signal at a multiple of that frequency.216 ### Optical modulator When the Fermi level of graphene is tuned, its optical absorption can be changed. In 2011, researchers reported the first graphene-based optical modulator. Operating at 1.2 GHz without a temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6 μm) and small footprint (~25 μm2).217 ### Coolant additive Graphene's high thermal conductivity suggests that it could be used as an additive in coolants. Preliminary research work showed that 5% graphene by volume can enhance the thermal conductivity of a base fluid by 86%.218 Another application due to graphene's enhanced thermal conductivity was found in PCR.171 ### Reference material Graphene's properties suggest it as a reference material for characterizing electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white light.219 This property was used to define the conductivity of transparency that combines sheet resistance and transparency. This parameter was used to compare materials without the use of two independent parameters.220 ### Thermal management In 2011, researchers reported that a three-dimensional, vertically aligned, functionalized multilayer graphene architecture can be an approach for graphene-based thermal interfacial materials (TIMs) with superior thermal conductivity and ultra-low interfacial thermal resistance between graphene and metal.90 Graphene-metal composites can be utilized in thermal interface materials.155 ### Energy storage #### Supercapacitor Due to graphene's high surface area to mass ratio, one potential application is in the conductive plates of supercapacitors.221 In February 2013 researchers announced a novel technique to produce graphene supercapacitors based on the DVD burner reduction approach.222 #### Electrode for Li-ion batteries Stable Li-ion cycling has recently been demonstrated in bi- and few layer graphene films grown on nickel substrates,223 while single layer graphene films have been demonstrated as a protective layer against corrosion in battery components such as the battery case.224 This creates possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active material as well as the current collector.225 There are also silicon-graphene anode Li-ion batteries.226227 ### Engineered piezoelectricity Density functional theory simulations predict that depositing certain adatoms on graphene can render it piezoelectrically responsive to an electric field applied in the out-of-plane direction. This type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials and makes graphene a candidate for control and sensing in nanoscale devices.228 ### Biodevice Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.229 Energy of the electrons with wavenumber k in graphene, calculated in the Tight Binding-approximation. The unoccupied (occupied) states, colored in blue–red (yellow–green), touch each other without energy gap exactly at the above-mentioned six k-vectors. The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of 0.34 nm) layers as nanoelectrodes into a nanopore230 can solve a bottleneck for nanopore-based single-molecule DNA sequencing. On November 20, 2013 the Bill & Melinda Gates Foundation awarded100,000 to 'to develop new elastic composite materials for condoms containing nanomaterials like graphene'.231

Stacked graphene layers on a quartz substrate increased the absorption of millimeter (radio) waves by 90 per cent over 125 – 165 GHz bandwidth, extensible to microwave and low-terahertz frequencies, while remaining transparent to visible light. For example, graphene could be used as a coating for buildings or windows to block radio waves. Absorption is a result of mutually coupled Fabry-Perot resonators represented by each graphene-quartz substrate. A repeated transfer-and-etch process was used to control surface resistivity.232233

## Pseudo-relativistic theory

Graphene's electrical properties can be described by a conventional tight-binding model; in this model the energy of the electrons with wave vector k is54234

$E=\pm\sqrt{\gamma_0^2\left(1+4\cos^2{\frac{k_ya}{2}}+4\cos{\frac{k_ya}{2}} \cdot \cos{\frac{k_x\sqrt{3}a}{2}}\right)}$

with the nearest-neighbor hopping energy γ02.8 eV and the lattice constant a ≈ 2.46 Å. The conduction and valence band, respectively, correspond to the different signs in the above dispersion relation; they touch each other at six points, the "K-values". However, only two of these six 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. Since an elementary cell of the lattice has a basis of two atoms, the wave function even has an effective 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. This pseudo-relativistic description is restricted to the chiral limit, i.e., to vanishing rest mass M0, which leads to interesting additional features:54235

$v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).$

Here vF ~ 106 is the Fermi velocity in graphene, which replaces the velocity of light in the Dirac theory; $\vec{\sigma}$ is the vector of the Pauli matrices, $\psi(\mathbf{r})$ is the two-component wave function of the electrons, and E is their energy.115

## References

1. ^ "This Month in Physics History: October 22, 2004: Discovery of Graphene". APS News. Series II 18 (9): 2. 2009.
2. ^ "The Nobel Prize in Physics 2010". The Nobel Foundation. Retrieved 2013-12-03.
3. ^ H. P. Boehm, R. Setton, E. Stumpp (1994). "Nomenclature and terminology of graphite intercalation compounds". Pure and Applied Chemistry 66 (9): 1893–1901. doi:10.1351/pac199466091893.
4. ^ H. P. Boehm, A. Clauss, G. O. Fischer, U. Hofmann (1962). "Das Adsorptionsverhalten sehr dünner Kohlenstoffolien". Zeitschrift für anorganische und allgemeine Chemie 316 (3–4): 119–127. doi:10.1002/zaac.19623160303.
5. ^ Mouras, S. et al. (1987). "Synthesis of first stage graphite intercalation compounds with fluorides". Revue de Chimie Minerale 24: 572.
6. ^ Saito, R. et al. (1992). "Electronic structure of graphene tubules based on C60". Physical Review B 46 (3): 1804. Bibcode:1992PhRvB..46.1804S. doi:10.1103/PhysRevB.46.1804.
7. ^ Forbeaux, I. et al. (1998). "Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure". Physical Review B 58 (24): 16396. Bibcode:1998PhRvB..5816396F. doi:10.1103/PhysRevB.58.16396.
8. ^ Wang, S. et al. (2000). "A new carbonaceous material with large capacity and high efficiency for rechargeable Li-ion batteries". Journal of the Electrochemical Society 147 (7): 2498. doi:10.1149/1.1393559.
9. ^ "graphene layer". IUPAC Gold Book. International Union of Pure and Applied Chemistry. Retrieved 31 March 2012.
10. ^ Simpson, C. D. et al. (2002). "Synthesis of a Giant 222 Carbon Graphite Sheet". Chemistry – A European Journal 6 (6): 1424. doi:10.1002/1521-3765(20020315)8:6<1424::AID-CHEM1424>3.0.CO;2-Z.
11. ^ Sakamoto J. et al (2009). "Two-Dimensional Polymers: Just a Dream of Synthetic Chemists?". Angew. Chem. Int. Ed. 48 (16): 1030–69. doi:10.1002/anie.200801863. PMID 19130514.
12. ^ Geim A. (2009). "Graphene: Status and Prospects". Science 324 (5934): 1530–4. arXiv:0906.3799. Bibcode:2009Sci...324.1530G. doi:10.1126/science.1158877. PMID 19541989.
13. ^ a b Riedl C., Coletti C., Iwasaki T., Zakharov A.A., Starke U. (2009). "Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation". Physical Review Letters 103 (24): 246804. arXiv:0911.1953. Bibcode:2009PhRvL.103x6804R. doi:10.1103/PhysRevLett.103.246804. PMID 20366220.
14. ^ Brodie, B. C. (1859). "On the Atomic Weight of Graphite". Philosophical Transactions of the Royal Society of London 149: 249–259. Bibcode:1859RSPT..149..249B. JSTOR 108699.
15. ^ Debije P, Scherrer P (1916). "Interferenz an regellos orientierten Teilchen im Röntgenlicht I". Physikalische Zeitschrift 17: 277.
16. ^ Friedrich W (1913). "Eine neue Interferenzerscheinung bei Röntgenstrahlen". Physikalische Zeitschrift 14: 317.
17. ^ Hull AW (1917). "A New Method of X-ray Crystal Analysis". Phys. Rev. 10 (6): 661. Bibcode:1917PhRv...10..661H. doi:10.1103/PhysRev.10.661.
18. ^ Kohlschütter, V.; Haenni, P. (1919). "Zur Kenntnis des Graphitischen Kohlenstoffs und der Graphitsäure". Zeitschrift für anorganische und allgemeine Chemie 105 (1): 121–144. doi:10.1002/zaac.19191050109.
19. ^ Bernal JD (1924). "The Structure of Graphite". Proc. R. Soc. Lond. A106 (740): 749–773. JSTOR 94336.
20. ^ Hassel O, Mack H (1924). "Über die Kristallstruktur des Graphits". Zeitschrift für Physik 25: 317. Bibcode:1924ZPhy...25..317H. doi:10.1007/BF01327534.
21. ^ DiVincenzo, D. P. and Mele, E. J. (1984). "Self-Consistent Effective Mass Theory for Intralayer Screening in Graphite Intercalation Compounds". Physical Review B 295 (4): 1685. Bibcode:1984PhRvB..29.1685D. doi:10.1103/PhysRevB.29.1685.
22. Novoselov, K. S. et al. (2005). "Two-dimensional gas of massless Dirac fermions in graphene". Nature 438 (7065): 197–200. arXiv:cond-mat/0509330. Bibcode:2005Natur.438..197N. doi:10.1038/nature04233. PMID 16281030.
23. ^ a b Gusynin, V. P. and Sharapov, S. G. (2005). "Unconventional Integer Quantum Hall Effect in Graphene". Physical Review Letters 95 (14): 146801. arXiv:cond-mat/0506575. Bibcode:2005PhRvL..95n6801G. doi:10.1103/PhysRevLett.95.146801. PMID 16241680.
24. ^ a b c Zhang, Y., Tan, Y. W., Stormer, H. L., and Kim, P. (2005). "Experimental observation of the quantum Hall effect and Berry's phase in graphene". Nature 438 (7065): 201–204. arXiv:cond-mat/0509355. Bibcode:2005Natur.438..201Z. doi:10.1038/nature04235. PMID 16281031.
25. ^ Ruess, G.; Vogt, F. (1948). "Höchstlamellarer Kohlenstoff aus Graphitoxyhydroxyd". Monatshefte für Chemie 78 (3–4): 222. doi:10.1007/BF01141527.
26. ^ a b c d Meyer, J. et al. (2007). "The structure of suspended graphene sheets". Nature 446 (7131): 60–63. arXiv:cond-mat/0701379. Bibcode:2007Natur.446...60M. doi:10.1038/nature05545. PMID 17330039.
27. ^ a b Boehm, H. P.; Clauss, A.; Fischer, G.; Hofmann, U. (1962). Proceedings of the Fifth Conference on Carbon. Pergamon Press.
28. ^ This paper reports graphitic flakes that give an additional contrast equivalent of down to ~0.4 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.26 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 & Novoselov 2007
29. ^ Oshima, C. and Nagashima, A. (1997). "Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces". J. Phys.: Condens. Matter 9: 1. Bibcode:1997JPCM....9....1O. doi:10.1088/0953-8984/9/1/004.
30. ^ a b c Geim, A. K.; Kim, P. (April 2008). "Carbon Wonderland". Scientific American. Retrieved 2009-05-05. "... bits of graphene are undoubtedly present in every pencil mark"
31. ^ United States Patent: 7071258. Patft.uspto.gov. Retrieved on 2014-01-12.
32. ^ a b Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. (2004). "Electric Field Effect in Atomically Thin Carbon Films". Science 306 (5696): 666–669. arXiv:cond-mat/0410550. Bibcode:2004Sci...306..666N. doi:10.1126/science.1102896. PMID 15499015.
33. ^ Kopelevich,, Y.; Torres, J.; Da Silva, R.; Mrowka, F.; Kempa, H.; Esquinazi, P. (2003). "Reentrant Metallic Behavior of Graphite in the Quantum Limit". Physical Review Letters 90 (15): 156402. arXiv:cond-mat/0209406. Bibcode:2003PhRvL..90o6402K. doi:10.1103/PhysRevLett.90.156402. PMID 12732058.
34. ^ Igor A. Luk’yanchuk and Yakov Kopelevich, Igor; Kopelevich, Yakov (2004). "Phase Analysis of Quantum Oscillations in Graphite". Physical Review Letters 93 (16): 166402. arXiv:cond-mat/0402058. Bibcode:2004PhRvL..93p6402L. doi:10.1103/PhysRevLett.93.166402. PMID 15525015.
35. ^ "Graphene pioneers bag Nobel prize". Institute of Physics, UK. October 5, 2010. Retrieved October 6, 2010.
36. ^ a b Carlsson, J. M. (2007). "Graphene: Buckle or break". Nature Materials 6 (11): 801–2. Bibcode:2007NatMa...6..801C. doi:10.1038/nmat2051. PMID 17972931.
37. ^ a b Fasolino, A., Los, J. H., & Katsnelson, M. I. (2007). "Intrinsic ripples in graphene". Nature Materials 6 (11): 858–61. arXiv:0704.1793. Bibcode:2007NatMa...6..858F. doi:10.1038/nmat2011. PMID 17891144.
38. ^ a b Ishigami, Masa; et al. (2007). "Atomic Structure of Graphene on SiO2". Nano Lett 7 (6): 1643–1648. Bibcode:2007NanoL...7.1643I. doi:10.1021/nl070613a. PMID 17497819.
39. ^ Stolyarova, Elena; et al. (2007). "High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface". Proceedings of the National Academy of Sciences 104 (22): 9209–9212. arXiv:0705.0833. Bibcode:2007PNAS..104.9209S. doi:10.1073/pnas.0703337104. PMC 1874226. PMID 17517635.
40. ^ Kasuya, D.; Yudasaka, M.; Takahashi, K.; Kokai, F.; Iijima, S. (2002). "Selective Production of Single-Wall Carbon Nanohorn Aggregates and Their Formation Mechanism". J. Phys. Chem. B 106 (19): 4947. doi:10.1021/jp020387n.
41. ^ Bernatowicz; T. J. et al. (1996). "Constraints on stellar grain formation from presolar graphite in the Murchison meteorite". Astrophysical Journal 472 (2): 760–782. Bibcode:1996ApJ...472..760B. doi:10.1086/178105.
42. ^ Fraundorf, P. and Wackenhut, M. (2002). "The core structure of presolar graphite onions". Astrophysical Journal Letters 578 (2): L153–156. arXiv:astro-ph/0110585. Bibcode:2002ApJ...578L.153F. doi:10.1086/344633.
43. ^ Recep Zan, Quentin M. Ramasse, Ursel Bangert, Konstantin S. Novoselov (2012). "Graphene re-knits its holes". Mesoscale and Nanoscale Physics 12 (8): 3936. arXiv:1207.1487v1. Bibcode:2012NanoL..12.3936Z. doi:10.1021/nl300985q.
44. ^ Puiu, Tibi (July 12, 2012) Graphene sheets can repair themselves naturally. zmescience.com
45. ^ Denis, P. A.; Iribarne F. (2013). "Comparative Study of Defect Reactivity in Graphene". Journal of Physical Chemistry C 117 (37): 19048. doi:10.1021/jp4061945.
46. ^ Yamada, Y.; Murota, K; Fujita, R; Kim, J; et al. "Subnanometer vacancy defects introduced on graphene by oxygen gas". Journal of American Chemical Society. doi:10.1021/ja4117268.
47. ^ Eftekhari, A.; Jafarkhani P. (2013). "Curly Graphene with Specious Interlayers Displaying Superior Capacity for Hydrogen Storage". Journal of Physical Chemistry C 117 (48): 25845. doi:10.1021/jp410044v.
48. ^ a b Yamada, Y.; Yasuda, H.; Murota, K.; Nakamura, M.; Sodesawa, T.; Sato, S. (2013). "Analysis of heat-treated graphite oxide by X-ray photoelectron spectroscopy". Journal of Material Science 48 (23): 8171. doi:10.1007/s10853-013-7630-0.
49. ^ Yamada, Y.; Kim, J.; Murota, K.; Matsuo, S.; Sato, S. "Nitrogen-containing graphene analyzed by X-ray photoelectron spectroscopy". Carbon. doi:10.1016/j.carbon.2013.12.061.
50. ^ "Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected". Phys.org. 1 February 2013. Retrieved 1 February 2013.
51. ^ Raji Heyrovska (2008). "Atomic Structures of Graphene, Benzene and Methane with Bond Lengths as Sums of the Single, Double and Resonance Bond Radii of Carbon". arXiv:0804.4086 physics.gen-ph.
52. ^ a b c d Charlier, J.-C.; Eklund, P.C.; Zhu, J. and Ferrari, A.C. (2008). "Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes". from Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications, Ed. A. Jorio, G. Dresselhaus, and M.S. Dresselhaus. Berlin/Heidelberg: Springer-Verlag.
53. Semenoff, G. W. (1984). "Condensed-Matter Simulation of a Three-Dimensional Anomaly". Physical Review Letters 53 (26): 2449. Bibcode:1984PhRvL..53.2449S. doi:10.1103/PhysRevLett.53.2449.
54. ^ a b Avouris, P., Chen, Z., and Perebeinos, V. (2007). "Carbon-based electronics". Nature Nanotechnology 2 (10): 605–15. Bibcode:2007NatNa...2..605A. doi:10.1038/nnano.2007.300. PMID 18654384.
55. [1]
56. ^ Baringhaus, J.; Ruan, M.; Edler, F.; Tejeda, A.; Sicot, M.; Taleb-Ibrahimi, A.; Li, A. P.; Jiang, Z.; Conrad, E. H.; Berger, C.; Tegenkamp, C.; De Heer, W. A. (2014). "Exceptional ballistic transport in epitaxial graphene nanoribbons". Nature 506 (7488): 349. doi:10.1038/nature12952.
57. ^ a b c Fuhrer, M. S. (2013). "Critical Mass in Graphene". Science 340 (6139): 1413–1414. doi:10.1126/science.1240317. PMID 23788788.
58. ^ Morozov, S.V. et al. (2008). "Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer". Physical Review Letters 100 (1): 016602. arXiv:0710.5304. Bibcode:2008PhRvL.100a6602M. doi:10.1103/PhysRevLett.100.016602. PMID 18232798.
59. ^ a b c Chen, J. H. et al. (2008). "Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2". Nature Nanotechnology 3 (4): 206–9. doi:10.1038/nnano.2008.58. PMID 18654504.
60. ^ Akturk, A. and Goldsman, N. (2008). "Electron transport and full-band electron–phonon interactions in graphene". Journal of Applied Physics 103 (5): 053702. Bibcode:2008JAP...103e3702A. doi:10.1063/1.2890147.
61. ^ Physicists Show Electrons Can Travel More Than 100 Times Faster in Graphene :: University Communications Newsdesk, University of Maryland. Newsdesk.umd.edu (2008-03-24). Retrieved on 2014-01-12.
62. ^ a b c Chen, J. H. et al. (2008). "Charged Impurity Scattering in Graphene". Nature Physics 4 (5): 377–381. arXiv:0708.2408. Bibcode:2008NatPh...4..377C. doi:10.1038/nphys935.
63. ^ a b c Schedin, F. et al. (2007). "Detection of individual gas molecules adsorbed on graphene". Nature Materials 6 (9): 652–655. Bibcode:2007NatMa...6..652S. doi:10.1038/nmat1967. PMID 17660825.
64. ^ Adam, S. et al. (2007). "A self-consistent theory for graphene transport". Proc. Nat. Acad. Sci. USA 104 (47): 18392–7. arXiv:0705.1540. Bibcode:2007PNAS..10418392A. doi:10.1073/pnas.0704772104. PMC 2141788. PMID 18003926.
65. ^ Hadar Steinberg, Gilad Barak, Amir Yacoby, et al (2008). "Charge fractionalization in quantum wires (Letter)". Nature Physics 4 (2): 116–119. arXiv:0803.0744. Bibcode:2008NatPh...4..116S. doi:10.1038/nphys810.
66. ^ Agung Trisetyarso (2012). "Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force". Quantum Information & Computation 12 (11–12): 989. arXiv:1003.4590. Bibcode:2010arXiv1003.4590T.
67. ^ Jiannis K. Pachos (2009). "Manifestations of topological effects in graphene". Contemporary Physics 50 (2): 375. arXiv:0812.1116. Bibcode:2009ConPh..50..375P. doi:10.1080/00107510802650507.
Fractionalization of charge and statistics in graphene and related structures, M. Franz, University of British Columbia, January 5, 2008
68. ^ Kuzmenko, A. B.; Van Heumen, E.; Carbone, F.; Van Der Marel, D. (2008). "Universal infrared conductance of graphite". Physical Review Letters 100 (11): 117401. arXiv:0712.0835. Bibcode:2008PhRvL.100k7401K. doi:10.1103/PhysRevLett.100.117401. PMID 18517825.
69. ^ Nair, R. R. et al. (2008). "Fine Structure Constant Defines Visual Transparency of Graphene". Science 320 (5881): 1308. Bibcode:2008Sci...320.1308N. doi:10.1126/science.1156965. PMID 18388259. [2]
70. ^ "Graphene Gazing Gives Glimpse Of Foundations Of Universe". ScienceDaily. 2008-04-04. Retrieved 2008-04-06.
71. ^ Zhang, Y. et al. (11 June 2009). "Direct observation of a widely tunable bandgap in bilayer graphene". Nature 459 (7248): 820–823. Bibcode:2009Natur.459..820Z. doi:10.1038/nature08105. PMID 19516337.
72. ^ Junfeng Liu, A. R. Wright, Chao Zhang, and Zhongshui Ma (29 July 2008). "Strong terahertz conductance of graphene nanoribbons under a magnetic field". Appl Phys Lett 93 (4): 041106–041110. Bibcode:2008ApPhL..93d1106L. doi:10.1063/1.2964093.
73. ^ a b Kurum, U. et al. (2011). "Electrochemically tunable ultrafast optical response of graphene oxide". Applied Physics Letters 98 (2): 141103. Bibcode:2011ApPhL..98b1103M. doi:10.1063/1.3540647.
74. ^ K.V.Sreekanth et al.; Zeng, Shuwen; Shang, Jingzhi; Yong, Ken-Tye; Yu, Ting (2012). "Excitation of surface electromagnetic waves in a graphene-based Bragg grating". Scientific Reports 2. Bibcode:2012NatSR...2E.737S. doi:10.1038/srep00737.
75. ^ Bao, Qiaoliang et al. (2009). "Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers". Advanced Functional Materials 19 (19): 3077. doi:10.1002/adfm.200901007. Archived from the original on 2011-07-17.
Zhang, H. et al.; Tang, D. Y.; Zhao, L. M.; Bao, Q. L.; Loh, K. P. (2009). "Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene". Optics Express 17 (20): P17630. arXiv:0909.5536. Bibcode:2009OExpr..1717630Z. doi:10.1364/OE.17.017630. Archived from the original on 2011-07-17.
Zhang, H. et al.; Bao, Qiaoliang; Tang, Dingyuan; Zhao, Luming; Loh, Kianping (2009). "Large energy soliton erbium-doped ﬁber laser with a graphene-polymer composite mode locker". Applied Physics Letters 95 (14): P141103. arXiv:0909.5540. Bibcode:2009ApPhL..95n1103Z. doi:10.1063/1.3244206. Archived from the original on 2011-07-17.
Zhang, H. et al. (2010). "Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser". Applied Physics Letters 96 (11): 111112. arXiv:1003.0154. Bibcode:2010ApPhL..96k1112Z. doi:10.1063/1.3367743. Archived from the original on 2010-05-21., Zhang (2009). "Graphene: Mode-locked lasers". NPG Asia Materials. doi:10.1038/asiamat.2009.52.
76. ^ Zheng, Z. et al. (2012). "Microwave and optical saturable absorption in graphene" (PDF). Optics Express 20 (21): 23201–23214. Bibcode:2012OExpr..2023201Z. doi:10.1364/OE.20.023201. PMID 23188285.
77. ^ Zhang, H. et al. (2012). "Z-scan measurement of the nonlinear refractive index of graphene". Optics Letters 37 (11): 1856–1858. Bibcode:2012OptL...37.1856Z. doi:10.1364/OL.37.001856. PMID 22660052.
78. ^ Onida, Giovanni; Rubio, Angel (2002). "Electronic excitations: Density-functional versus many-body Green's-function approaches". Rev. Mod. Phys. 74 (2): 601. Bibcode:2002RvMP...74..601O. doi:10.1103/RevModPhys.74.601.
79. ^ Yang, Li; Deslippe, Jack; Park, Cheol-Hwan; Cohen, Marvin; Louie, Steven (2009). "Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene". Physical Review Letters 103 (18): 186802. arXiv:0906.0969. Bibcode:2009PhRvL.103r6802Y. doi:10.1103/PhysRevLett.103.186802. PMID 19905823.
80. ^ Prezzi, Deborah; Varsano, Daniele; Ruini, Alice; Marini, Andrea; Molinari, Elisa (2008). "Optical properties of graphene nanoribbons: The role of many-body effects". Physical Review B 77 (4): 041404. arXiv:0706.0916. Bibcode:2008PhRvB..77d1404P. doi:10.1103/PhysRevB.77.041404.
Yang, Li; Cohen, Marvin L.; Louie, Steven G. (2007). "Excitonic Effects in the Optical Spectra of Graphene Nanoribbons". Nano Lett. 7 (10): 3112–5. arXiv:0707.2983. Bibcode:2007NanoL...7.3112Y. doi:10.1021/nl0716404. PMID 17824720.
Yang, Li; Cohen, Marvin L.; Louie, Steven G. (2008). "Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons". Physical Review Letters 101 (18): 186401. Bibcode:2008PhRvL.101r6401Y. doi:10.1103/PhysRevLett.101.186401. PMID 18999843.
81. ^ Zhu, Xi; Su, Haibin (2010). "Excitons of Edge and Surface Functionalized Graphene Nanoribbons". J. Phys. Chem. C 114 (41): 17257. doi:10.1021/jp102341b.
82. ^ Wang, Min; Li, Chang Ming (2011). "Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons". Nanoscale 3 (5): 2324–8. Bibcode:2011Nanos...3.2324W. doi:10.1039/c1nr10095e. PMID 21503364.
83. ^ Dima Bolmatov, Chung-Yu Mou (2010). "Josephson effect in graphene SNS junction with a single localized defect". Physica B 405 (13): 2896. arXiv:1006.1391. Bibcode:2010PhyB..405.2896B. doi:10.1016/j.physb.2010.04.015.
Dima Bolmatov, Chung-Yu Mou (2010). "Tunneling conductance of the graphene SNS junction with a single localized defect". Journal of Experimental and Theoretical Physics (JETP) 110 (4): 613. arXiv:1006.1386. Bibcode:2010JETP..110..613B. doi:10.1134/S1063776110040084.
84. ^ Zhu, Xi; Su, Haibin (2011). "Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges". Journal of Physical Chemistry A 115 (43): 11998–12003. doi:10.1021/jp202787h.
85. ^ O. B. Shenderova, V. V. Zhirnov, D. W. Brenner (2002). "Carbon Nanostructures". Critical Reviews in Solid State and Materials Sciences 27 (3–4): 227. Bibcode:2002CRSSM..27..227S. doi:10.1080/10408430208500497.
86. ^ Chen, Shanshan; Wu, Qingzhi; Mishra, Columbia; Kang, Junyong; Zhang, Hengji; Cho, Kyeongjae; Cai, Weiwei; Balandin, Alexander A. et al. (2012). "Thermal conductivity of isotopically modified graphene". Nature Materials (2012-01-10) 11 (3): 203. arXiv:1112.5752. Bibcode:2012NatMa..11..203C. doi:10.1038/nmat3207.
Lay summary: Suzanne Tracy (2012-01-12). "Keeping Electronics Cool". Scientific Computing (Advantage Business Media). scientificcomputing.com. Retrieved 2012-01-15.
87. ^ Balandin, A. A. et al. (2008-02-20). "Superior Thermal Conductivity of Single-Layer Graphene". Nano Letters ASAP 8 (3): 902–907. Bibcode:2008NanoL...8..902B. doi:10.1021/nl0731872. PMID 18284217.
88. ^ Saito, K., Nakamura, J., and Natori, A. (2007). "Ballistic thermal conductance of a graphene sheet". Physical Review B 76 (11): 115409. Bibcode:2007PhRvB..76k5409S. doi:10.1103/PhysRevB.76.115409.
89. ^ a b Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. (2011). "A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials". ACS Nano 5 (3): 2392–2401. doi:10.1021/nn200181e. PMID 21384860.
90. ^ Delhaes, P. (2001). Graphite and Precursors. CRC Press. ISBN 90-5699-228-7.
91. ^ a b Mingo N., Broido, D.A. (2005). "Carbon Nanotube Ballistic Thermal Conductance and Its Limits". Physical Review Letters 95 (9): 096105. Bibcode:2005PhRvL..95i6105M. doi:10.1103/PhysRevLett.95.096105.
92. ^ Mounet, N. and Marzari, N. (2005). "First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives". Physical Review B 71 (20): 205214. arXiv:cond-mat/0412643. Bibcode:2005PhRvB..71t5214M. doi:10.1103/PhysRevB.71.205214.
93. ^ Lifshitz, I.M. (1952). Journal of Experimental and Theoretical Physics (in Russian) 22: 475.
94. ^ S. Braga, V. R. Coluci, S. B. Legoas, R. Giro, D. S. Galvão, R. H. Baughman (2004). "Structure and Dynamics of Carbon Nanoscrolls". Nano Letters 4 (5): 881. Bibcode:2004NanoL...4..881B. doi:10.1021/nl0497272.
95. ^ a b 2010 Nobel Physics Laureates. nobelprize.org.
96. ^ Lee, C. et al. (2008). "Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene". Science 321 (5887): 385–8. Bibcode:2008Sci...321..385L. doi:10.1126/science.1157996. PMID 18635798. Lay summary.
97. ^ Sanderson, Bill (2008-08-25). "Toughest Stuff Known to Man: Discovery Opens Door to Space Elevator". nypost.com. Retrieved 2008-10-09.
98. ^ "Breakthrough in Developing Super-Material Graphene". ScienceDaily. 2010-01-20. Retrieved 2010-02-21.
99. ^ Frank, I. W., Tanenbaum, D. M., Van Der Zande, A.M., and McEuen, P. L. (2007). "Mechanical properties of suspended graphene sheets". J. Vac. Sci. Technol. B 25 (6): 2558–2561. Bibcode:2007JVSTB..25.2558F. doi:10.1116/1.2789446.
100. ^ Dima Bolmatov and Chung-Yu Mou (2011). "Graphene-based modulation-doped superlattice structures". Journal of Experimental and Theoretical Physics (JETP) 112: 102. arXiv:1011.2850. Bibcode:2011JETP..112..102B. doi:10.1134/S1063776111010043.
Dima Bolmatov (2011). "Thermodynamic properties of tunneling quasiparticles in graphene-based structures". Physica C 471 (23–24): 1651. arXiv:1106.6331. Bibcode:2011PhyC..471.1651B. doi:10.1016/j.physc.2011.07.008.
101. ^ a b Tombros, Nikolaos; et al. (2007). "Electronic spin transport and spin precession in single graphene layers at room temperature". Nature (PDF) 448 (7153): 571–575. arXiv:0706.1948. Bibcode:2007Natur.448..571T. doi:10.1038/nature06037. PMID 17632544.
102. ^ a b Cho, Sungjae; Yung-Fu Chen, and Michael S. Fuhrer (2007). "Gate-tunable Graphene Spin Valve". Applied Physics Letters 91 (12): 123105. arXiv:0706.1597. Bibcode:2007ApPhL..91l3105C. doi:10.1063/1.2784934.
103. ^ Ohishi, Megumi; et al. (2007). "Spin Injection into a Graphene Thin Film at Room Temperature". Jpn J Appl Phys 46: L605–L607. arXiv:0706.1451. Bibcode:2007JaJAP..46L.605O. doi:10.1143/JJAP.46.L605.
104. ^ a b c Kim, Kuen Soo; et al. (2009). "Large-scale pattern growth of graphene films for stretchable transparent electrodes". Nature 457 (7230): 706–10. Bibcode:2009Natur.457..706K. doi:10.1038/nature07719. PMID 19145232.
105. ^ a b Johannes Jobst, Daniel Waldmann, Florian Speck, Roland Hirner, Duncan K. Maude, Thomas Seyller, Heiko B. Weber (2009). "How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect". Physical Review B 81 (19). arXiv:0908.1900. Bibcode:2010PhRvB..81s5434J. doi:10.1103/PhysRevB.81.195434.
106. ^ a b T. Shen, J.J. Gu, M. Xu, Y.Q. Wu, M.L. Bolen, M.A. Capano, L.W. Engel, P.D. Ye (2009). "Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001)". Applied Physics Letters 95 (17): 172105. arXiv:0908.3822. Bibcode:2009ApPhL..95q2105S. doi:10.1063/1.3254329.
107. ^ a b Xiaosong Wu, Yike Hu, Ming Ruan, Nerasoa K Madiomanana, John Hankinson, Mike Sprinkle, Claire Berger, Walt A. de Heer (2009). "Half integer quantum Hall effect in high mobility single layer epitaxial graphene". Applied Physics Letters 95 (22): 223108. arXiv:0909.2903. Bibcode:2009ApPhL..95v3108W. doi:10.1063/1.3266524.
108. ^ a b Samuel Lara-Avila, Alexei Kalaboukhov, Sara Paolillo, Mikael Syväjärvi, Rositza Yakimova, Vladimir Fal'ko, Alexander Tzalenchuk, Sergey Kubatkin (2009). "SiC Graphene Suitable For Quantum Hall Resistance Metrology". Nature Nanotechnology 5 (3): 186–9. arXiv:0909.1193. Bibcode:2010NatNa...5..186T. doi:10.1038/nnano.2009.474. PMID 20081845.
109. ^ a b J.A. Alexander-Webber, A.M.R. Baker, T.J.B.M. Janssen, A. Tzalenchuk, S. Lara-Avila, S. Kubatkin, R. Yakimova, B. A. Piot, D. K. Maude, and R.J. Nicholas (2013). "Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene". Physical Review Letters 111 (9): 096601. arXiv:1304.4897. Bibcode:2013PhRvL.111i6601A. doi:10.1103/PhysRevLett.111.096601. PMID 24033057.
110. ^ Michael S. Fuhrer (2009). "A physicist peels back the layers of excitement about graphene". Nature 459 (7250): 1037. Bibcode:2009Natur.459.1037F. doi:10.1038/4591037e. PMID 19553953.
111. ^ Zhang, Y. et al. (2006). "Landau-Level Splitting in Graphene in High Magnetic Fields". Physical Review Letters 96 (13): 136806. arXiv:cond-mat/0602649. Bibcode:2006PhRvL..96m6806Z. doi:10.1103/PhysRevLett.96.136806.
112. ^ a b Du, X. et al. (2009). "Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene". Nature 462 (7270): 192–195. arXiv:0910.2532. Bibcode:2009Natur.462..192D. doi:10.1038/nature08522. PMID 19829294.
113. ^ Bolotin, K. et al. (2009). "Observation of the fractional quantum Hall effect in graphene". Nature 462 (7270): 196–199. arXiv:0910.2763. Bibcode:2009Natur.462..196B. doi:10.1038/nature08582. PMID 19881489.
114. ^ a b A Castro Neto, et al. (2009). "The electronic properties of graphene". Rev Mod Phys 81: 109. arXiv:0709.1163. Bibcode:2009RvMP...81..109C. doi:10.1103/RevModPhys.81.109.
115. ^ "Graphene Oxide Paper". Northwestern University. Archived from the original on 2011-07-20. Retrieved 2011-02-28.
116. ^ Eftekhari, Ali; Yazdani, Bahareh (2010). "Initiating electropolymerization on graphene sheets in graphite oxide structure". Journal of Polymer Science Part A: Polymer Chemistry 48 (10): 2204. Bibcode:2010JPoSA..48.2204E. doi:10.1002/pola.23990.
117. ^ Nalla, Venkatram; Polavarapu, L; Manga, KK; Goh, BM; Loh, KP; Xu, QH; Ji, W (2010). "Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite". Nanotechnology 21 (41): 415203. Bibcode:2010Nanot..21O5203N. doi:10.1088/0957-4484/21/41/415203. PMID 20852355.
118. ^ a b Nair, R. R.; Wu, H. A.; Jayaram, P. N.; Grigorieva, I. V.; Geim, A. K. (2012). "Unimpeded permeation of water through helium-leak-tight graphene-based membranes". Science 335 (6067): 442–4. arXiv:1112.3488. Bibcode:2012Sci...335..442N. doi:10.1126/science.1211694. PMID 22282806.
119. ^ Sandip Niyogi, Elena Bekyarova, Mikhail E. Itkis, Jared L. McWilliams, Mark A. Hamon, and Robert C. Haddon (2006). "Solution Properties of Graphite and Graphene". J. Am. Chem. Soc. 128 (24): 7720–7721. doi:10.1021/ja060680r. PMID 16771469.
120. ^ Raymond L.D. Whitby, Alina Korobeinyk, and Katya V. Glevatska (2011). "Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry". Carbon 49 (2): 722–725. doi:10.1016/j.carbon.2010.09.049.
121. ^ Sungjin Park, Dmitriy A. Dikin, SonBinh T. Nguyen, and Rodney S. Ruoff (2009). "Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine". J. Phys. Chem. C 113 (36): 15801–15804. doi:10.1021/jp907613s.
122. ^ D. C. Elias et al. (2009). "Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane". Science 323 (5914): 610–3. arXiv:0810.4706. Bibcode:2009Sci...323..610E. doi:10.1126/science.1167130. PMID 19179524.
123. ^ Bordag M., Fialkovsky I. V., Gitman D. M., Vassilevich D. V. (2009). "Casimir interaction between a perfect conductor and graphene described by the Dirac model". Physical Review B 80 (24): 245406. arXiv:0907.3242. Bibcode:2009PhRvB..80x5406B. doi:10.1103/PhysRevB.80.245406.
124. ^ Fialkovsky I. V., Marachevskiy V.N., Vassilevich D. V.; Marachevsky; Vassilevich (2011). "Finite temperature Casimir effect for graphene". Physical Review B 84 (35446): 35446. arXiv:1102.1757. Bibcode:2011PhRvB..84c5446F. doi:10.1103/PhysRevB.84.035446.
125. ^ Dobson J. F., White A., Rubio A. (2006). "Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals". Physical Review Letters 96 (7): 073201. arXiv:cond-mat/0502422. Bibcode:2006PhRvL..96g3201D. doi:10.1103/PhysRevLett.96.073201.
126. ^ Min, Hongki; Sahu, Bhagawan; Banerjee, Sanjay; MacDonald, A. (2007). "Ab initio theory of gate induced gaps in graphene bilayers". Physical Review B 75 (15). arXiv:cond-mat/0612236. Bibcode:2007PhRvB..75o5115M. doi:10.1103/PhysRevB.75.155115.
127. ^ Barlas, Yafis; Côté, R.; Lambert, J.; MacDonald, A. H. (2010). "Anomalous Exciton Condensation in Graphene Bilayers". Physical Review Letters 104 (9). arXiv:0909.1502. Bibcode:2010PhRvL.104i6802B. doi:10.1103/PhysRevLett.104.096802.
128. ^ Min, Lola; Hovden, Robert; Huang, Pinshane; Wojcik, Michal; Muller, David A.; Park, Jiwoong (2012). "Twinning and Twisting of Tri- and Bilayer Graphene". NanoLetters 12 (3): 1609. Bibcode:2012NanoL..12.1609B. doi:10.1021/nl204547v.
129. ^ Wang, H.; Sun, K.; Tao, F.; Stacchiola, D. J.; Hu, Y. H. (2013). "3D Honeycomb-Like Structured Graphene and Its High Efficiency as a Counter-Electrode Catalyst for Dye-Sensitized Solar Cells". Angewandte Chemie 125 (35): 9380. doi:10.1002/ange.201303497.
Wang, Hui; Sun, Kai; Tao, Franklin; Stacchiola, Dario J.; Hu, Yun Hang. "3D graphene could replace expensive platinum in solar cells". Angewandte Chemie (KurzweilAI) 125 (35): 9380. Retrieved 2013-08-24.
130. ^ a b Geim, A. K. & MacDonald, A. H. (2007). "Graphene: Exploring carbon flatland". Physics Today 60 (8): 35–41. Bibcode:2007PhT....60h..35G. doi:10.1063/1.2774096.
131. ^
Waszak, S. (April 2011). "Polish team claims leap for wonder material graphene". Phys.org.
132. ^ Gall, N. R.; Rut'Kov, E. V.; Tontegode, A. Ya. (1997). "Two Dimensional Graphite Films on Metals and Their Intercalation". International Journal of Modern Physics B 11 (16): 1865. Bibcode:1997IJMPB..11.1865G. doi:10.1142/S0217979297000976.
133. ^ Gall, N. R.; Rut'Kov, E. V.; Tontegode, A. Ya. (1995). "Influence of surface carbon on the formation of silicon-refractory metal interfaces". Thin Solid Films 266 (2): 229. Bibcode:1995TSF...266..229G. doi:10.1016/0040-6090(95)06572-5.
134. ^ Sutter, P. (2009). "Epitaxial graphene: How silicon leaves the scene". Nature Materials 8 (3): 171–2. Bibcode:2009NatMa...8..171S. doi:10.1038/nmat2392. PMID 19229263.
135. ^ a b Ohta, T. et al. (2007). "Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy". Physical Review Letters 98 (20): 206802. Bibcode:2007PhRvL..98t6802O. doi:10.1103/PhysRevLett.98.206802. PMID 17677726.
136. ^ a b Bostwick, A. et al. (2007). "Symmetry breaking in few layer graphene films". New Journal of Physics 9 (10): 385. arXiv:0705.3705. Bibcode:2007NJPh....9..385B. doi:10.1088/1367-2630/9/10/385.
137. ^ Zhou, S.Y. (2006). "First direct observation of Dirac fermions in graphite". Nature Physics 2 (9): 595–599. arXiv:cond-mat/0608069. Bibcode:2006NatPh...2..595Z. doi:10.1038/nphys393.
138. ^ Morozov, S.V. et al. (2006). "Strong Suppression of Weak Localization in Graphene". Physical Review Letters 97 (1): 016801. arXiv:cond-mat/0603826. Bibcode:2006PhRvL..97a6801M. doi:10.1103/PhysRevLett.97.016801. PMID 16907394.
139. ^ a b Hass, J. et al. (2008). "Why multilayer graphene on 4H-SiC(000(1)over-bar) behaves like a single sheet of graphene". Physical Review Letters 100 (12): 125504. Bibcode:2008PhRvL.100l5504H. doi:10.1103/PhysRevLett.100.125504.
140. ^ Singh, Ram Sevak; Nalla, Venkatram; Chen, Wei; Wee, Andrew Thye Shen; Ji, Wei (2011). "Laser Patterning of Epitaxial Graphene for Schottky Junction Photodetectors". ACS Nano 5 (7): 5969–75. doi:10.1021/nn201757j. PMID 21702443.
141. ^ "A smarter way to grow graphene". PhysOrg.com. May 2008.
142. ^ Pletikosić, I. et al. (2009). "Dirac Cones and Minigaps for Graphene on Ir(111)". Physical Review Letters 102 (5): 056808. arXiv:0807.2770. Bibcode:2009PhRvL.102e6808P. doi:10.1103/PhysRevLett.102.056808.
143. ^ a b c Bae, S. et al. (2010). "Roll-to-roll production of 30-inch graphene films for transparent electrodes". Nature Nanotechnology 5 (8): 574–578. Bibcode:2010NatNa...5..574B. doi:10.1038/nnano.2010.132. PMID 20562870.
144. ^ J. Rafiee, X. Mi, H. Gullapalli, A.V. Thomas, F. Yavari, Y. Shi, P.M. Ajayan, N.A. Koratkar, Wetting transparency of graphene, Nature Materials, 11 (2012) 217-222.
145. ^ Li, Xuesong; et al. (2009). "Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils". Science 324 (5932): 1312–4. arXiv:0905.1712. Bibcode:2009Sci...324.1312L. doi:10.1126/science.1171245. PMID 19423775.
146. ^ Wassei, Jonathan K.; Mecklenburg, Matthew; Torres, Jaime A.; Fowler, Jesse D.; Regan, B. C.; Kaner, Richard B.; Weiller, Bruce H. (12 May 2012). "Chemical Vapor Deposition of Graphene on Copper from Methane, Ethane and Propane: Evidence for Bilayer Selectivity". Small 8 (9): 1415–1422. doi:10.1002/smll.201102276. PMID 22351509.
147. ^ Lenski, Daniel R.; Fuhrer, Michael S. (2011). "Raman and optical characterization of multilayer turbostratic graphene grown via chemical vapor deposition". Journal of Applied Physics 110: 013720. arXiv:1011.1683. Bibcode:2011JAP...110a3720L. doi:10.1063/1.3605545.
148. ^ Weatherup, R.S. et al. (2011). "In Situ Characterization of Alloy Catalysts for Low-Temperature Graphene Growth". Nano Letters 11 (10): 4154–60. Bibcode:2011NanoL..11.4154W. doi:10.1021/nl202036y. PMID 21905732.
149. ^ Boehm’s 1961 isolation of graphene. Graphene Times (2009-12-07). Retrieved on 2010-12-10.
150. ^ Letters to the Editor. Many Pioneers in Graphene Discovery. Aps.org. January 2010.
151. ^ S. Eigler, M. Enzelberger-Heim, S. Grimm, P. Hofmann, W. Kroener, A. Geworski, C. Dotzer, M. Röckert, J. Xiao, C. Papp, O. Lytken, H.-P. Steinrück, P. Müller, A. Hirsch (2013). "Wet Chemical Synthesis of Graphene". Advanced Materials 25 (26): 3583–3587. doi:10.1002/adma.201300155. PMID 23703794.
152. ^ Ji, L.; Xin, H. L.; Kuykendall, T. R.; Wu, S. L.; Zheng, H.; Rao, M.; Cairns, E. J.; Battaglia, V.; Zhang, Y. (2012). "SnS2 nanoparticle loaded graphene nanocomposites for superior energy storage". Physical Chemistry Chemical Physics 14 (19): 6981. doi:10.1039/C2CP40790F.
153. ^ "Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors". Sciencemag.org. 2012-03-16. Retrieved 2013-05-02.
Marcus, Jennifer (2012-03-15). "Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom". Newsroom.ucla.edu. Retrieved 2013-05-02.
154. ^ a b c Shaahin Amini, Javier Garay, Guanxiong Liu, Alexander A. Balandin, Reza Abbaschian (2010). "Growth of Large-Area Graphene Films from Metal-Carbon Melts". Journal of Applied Physics 108 (9): 094321. arXiv:1011.4081. Bibcode:2010JAP...108i4321A. doi:10.1063/1.3498815.
155. ^ Choucair, M.; Thordarson, P; Stride, JA (2008). "Gram-scale production of graphene based on solvothermal synthesis and sonication". Nature Nanotechnology 4 (1): 30–3. Bibcode:2009NatNa...4...30C. doi:10.1038/nnano.2008.365. PMID 19119279.
156. ^ Brumfiel, G. (2009). "Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons". Nature. doi:10.1038/news.2009.367.
157. ^ Kosynkin, D. V. et al. (2009). "Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons". Nature 458 (7240): 872–6. Bibcode:2009Natur.458..872K. doi:10.1038/nature07872. PMID 19370030.
158. ^ Liying Jiao, Li Zhang, Xinran Wang, Georgi Diankov & Hongjie Dai (2009). "Narrow graphene nanoribbons from carbon nanotubes". Nature 458 (7240): 877–80. Bibcode:2009Natur.458..877J. doi:10.1038/nature07919. PMID 19370031.
159. ^ Hernandez, Y.; Nicolosi, V.; Lotya, M.; Blighe, F. M.; Sun, Z.; De, S.; McGovern, I. T.; Holland, B.; Byrne, M.; Gun'Ko, Y. K.; Boland, J. J.; Niraj, P.; Duesberg, G.; Krishnamurthy, S.; Goodhue, R.; Hutchison, J.; Scardaci, V.; Ferrari, A. C.; Coleman, J. N. (2008). "High-yield production of graphene by liquid-phase exfoliation of graphite". Nature Nanotechnology 3 (9): 563–568. doi:10.1038/nnano.2008.215. PMID 18772919.
160. ^ Alzari, V.; Nuvoli, D.; Scognamillo, S.; Piccinini, M.; Gioffredi, E.; Malucelli, G.; Marceddu, S.; Sechi, M.; Sanna, V.; Mariani, A. (2011). "Graphene-containing thermoresponsive nanocomposite hydrogels of poly(N-isopropylacrylamide) prepared by frontal polymerization". Journal of Materials Chemistry 21 (24): 8727. doi:10.1039/C1JM11076D.
161. ^ Nuvoli, D.; Valentini, L.; Alzari, V.; Scognamillo, S.; Bon, S. B.; Piccinini, M.; Illescas, J.; Mariani, A. (2011). "High concentration few-layer graphene sheets obtained by liquid phase exfoliation of graphite in ionic liquid". Journal of Materials Chemistry 21 (10): 3428. doi:10.1039/C0JM02461A.
162. ^ Woltornist, S. J., Oyer, A. J., Carrillo, J.-M. Y., Dobrynin, A. V, & Adamson, D. H. (2013). Conductive thin films of pristine graphene by solvent interface trapping. ACS nano, 7(8), 7062–6. doi:10.1021/nn402371c
163. ^ Chakrabarti, A.; Lu, J.; Skrabutenas, J. C.; Xu, T.; Xiao, Z.; Maguire, J. A.; Hosmane, N. S. (2011). "Conversion of carbon dioxide to few-layer graphene". Journal of Materials Chemistry 21 (26): 9491. doi:10.1039/C1JM11227A.
164. ^ Monie, Sanjay. "Developments in Conductive Inks". Industrial & Specialty Printing. Retrieved 26 April 2010.
165. ^ Segal, M. (2009). "Selling graphene by the ton". Nature Nanotechnology 4 (10): 612–4. Bibcode:2009NatNa...4..612S. doi:10.1038/nnano.2009.279. PMID 19809441.
166. ^ Patel, P. (15 January 2009). "Bigger, Stretchier Graphene". MIT Technology Review.
167. ^ "EUROPA - PRESS RELEASES - Press Release - Graphene and Human Brain Project win largest research excellence award in history, as battle for sustained science funding continues". Europa.eu. 2013-01-28. Retrieved 2013-05-02.
168. ^ Thomson, Iain. "Nokia shares \$1.35bn EU graphene research grant". The Register.
"FET Graphene Flagship". Graphene-flagship.eu. Retrieved 2013-08-24.
169. ^ Sherriff, Lucy (2012-09-05). "Nokia dials into graphene in photo-sensor patent move". ZDNet. Retrieved 2013-08-24.
170. ^ a b r, A. K.; Kafafy, R.; Salleh, H. M.; Faris, W. F. (2012). "Enhancing the efficiency of polymerase chain reaction using graphene nanoflakes". Nanotechnology 23 (45): 455106. doi:10.1088/0957-4484/23/45/455106. PMID 23085573.
171. ^ Chen, J., Ishigami, M., Jang, C., Hines, D. R., Fuhrer, M. S., and Williams, E. D. (2007). "Printed graphene circuits". Advanced Materials 19 (21): 3623–3627. doi:10.1002/adma.200701059.
172. ^ a b Ponomarenko, L. A. et al. (2008). "Chaotic Dirac Billiard in Graphene Quantum Dots". Science 320 (5874): 356–8. arXiv:0801.0160. Bibcode:2008Sci...320..356P. doi:10.1126/science.1154663. PMID 18420930. Lay summary.
173. ^ "Graphene transistors clocked at 26 GHz Arxiv article". Arxivblog.com. 2008-12-11. Retrieved 2009-08-15.
174. ^ Wang, X.; Li, X.; Zhang, L.; Yoon, Y.; Weber, P. K.; Wang, H.; Guo, J.; Dai, H. (2009). "N-Doping of Graphene Through Electrothermal Reactions with Ammonia". Science 324 (5928): 768–71. Bibcode:2009Sci...324..768W. doi:10.1126/science.1170335. PMID 19423822. Lay summary.
175. ^
176. ^ Traversi, F.; Russo, V.; Sordan, R. (2009). "Integrated complementary graphene inverter". Appl. Phys. Lett. 94 (22): 223312. arXiv:0904.2745. Bibcode:2009ApPhL..94v3312T. doi:10.1063/1.3148342. Lay summary.
177. ^ "European collaboration breakthrough in developing graphene". NPL. 2010-01-19. Retrieved 2010-02-21.
178. ^ Lin, Y.-M.; Dimitrakopoulos, C.; Jenkins, K. A.; Farmer, D. B.; Chiu, H.-Y.; Grill, A.; Avouris, Ph. (2010). "100-GHz Transistors from Wafer-Scale Epitaxial Graphene". Science 327 (5966): 662–662. arXiv:1002.3845. Bibcode:2010Sci...327..662L. doi:10.1126/science.1184289. ISSN 0036-8075. PMID 20133565.
179. ^ Lin, Y.-M.; Valdes-Garcia, A.; Han, S.-J.; Farmer, D. B.; Meric, I.; Sun, Y.; Wu, Y.; Dimitrakopoulos, C.; Grill, A.; Avouris, P.; Jenkins, K. A. (2011). "Wafer-Scale Graphene Integrated Circuit". Science 332 (6035): 1294–1297. Bibcode:2011Sci...332.1294L. doi:10.1126/science.1204428. ISSN 0036-8075. PMID 21659599.
180. ^
181. ^
182. ^ Lemme, M. C. et al. (2007). "A graphene field-effect device". IEEE Electron Device Letters 28 (4): 282. arXiv:cond-mat/0703208. Bibcode:2007IEDL...28..282L. doi:10.1109/LED.2007.891668.
183. ^ Bullis, K. (2008-01-28). "Graphene Transistors". Cambridge: MIT Technology Review, Inc. Retrieved 2008-02-18.
184. ^ Kedzierski, J. et al. (2008). "Epitaxial Graphene Transistors on SiC Substrates". IEEE Transactions on Electron Devices 55 (8): 2078–2085. arXiv:0801.2744. Bibcode:2008ITED...55.2078K. doi:10.1109/TED.2008.926593.
185. ^ Moon, J.S. et al. (2009). "Epitaxial-Graphene RF Field-Effect Transistors on Si-Face 6H-SiC Substrates". IEEE Electron Device Letters 30 (6): 650–652. Bibcode:2009IEDL...30..650M. doi:10.1109/LED.2009.2020699.
186. ^ Echtermeyer, Tim. J. et al. (2008). "Nonvolatile Switching in Graphene Field-Effect Devices". IEEE Electron Device Letters 29 (8): 952. arXiv:0805.4095. Bibcode:2008IEDL...29..952E. doi:10.1109/LED.2008.2001179.
187. ^ Sordan, R.; Traversi, F.; Russo, V. (2009). "Logic gates with a single graphene transistor". Appl. Phys. Lett. 94 (7): 073305. Bibcode:2009ApPhL..94g3305S. doi:10.1063/1.3079663.
188. ^ Fiori G., Iannaccone G., "On the possibility of tunable-gap bilayer graphene FET", IEEE Electr. Dev. Lett., 30, 261 (2009)
189. ^ Fiori G., Iannaccone G., "Ultralow-Voltage Bilayer graphene tunnel FET", IEEE Electr. Dev. Lett., 30, 1096 (2009)
190. ^ Bourzac, Katherine (2010-02-05). "Graphene Transistors that Can Work at Blistering Speeds". MIT Technology Review.
191. ^ IBM shows off 100GHz graphene transistor – Techworld.com. News.techworld.com. Retrieved on 2010-12-10.
192. ^ Lin et al.; Dimitrakopoulos, C; Jenkins, KA; Farmer, DB; Chiu, HY; Grill, A; Avouris, P (2010). "100-GHz Transistors from Wafer-Scale Epitaxial Graphene". Science (Science) 327 (5966): 662. arXiv:1002.3845. Bibcode:2010Sci...327..662L. doi:10.1126/science.1184289. PMID 20133565.
193. ^ Ink-Jet Printed Graphene Electronics. Cornell University Library. Retrieved on 2011-29-11.
194. ^ Kawano, Yukio (2013). "Wide-band frequency-tunable terahertz and infrared detection with graphene". Nanotechnology 24 (21): 214004. Bibcode:2013Nanot..24u4004K. doi:10.1088/0957-4484/24/21/214004. PMID 23618878.
195. ^ Britnell, L.; Gorbachev, R. V.; Geim, A. K.; Ponomarenko, L. A.; Mishchenko, A.; Greenaway, M. T.; Fromhold, T. M.; Novoselov, K. S. et al. (2013). "Radical new graphene design operates at terahertz speed". Nature Communications (KurzweilAI) 4 (4): 1794–. arXiv:1303.6864. Bibcode:2013NatCo...4E1794B. doi:10.1038/ncomms2817. PMC 3644101. PMID 23653206. Retrieved 2013-05-02.
Britnell, L.; Gorbachev, R. V.; Geim, A. K.; Ponomarenko, L. A.; Mishchenko, A.; Greenaway, M. T.; Fromhold, T. M.; Novoselov, K. S.; Eaves, L. (2013). "Resonant tunnelling and negative differential conductance in graphene transistors". Nature Communications 4: 1794–. arXiv:1303.6864. Bibcode:2013NatCo...4E1794B. doi:10.1038/ncomms2817. PMC 3644101. PMID 23653206.
196. ^ Guanxiong Liu; Sonia Ahsan; Khitun, Alexander G.; Lake, Roger K.; Balandin, Alexander A. (2013). "Graphene-Based Non-Boolean Logic Circuits". Journal of Applied Physics, , (2013) 114 (10): 4310. arXiv:1308.2931. Bibcode:2013JAP...114o4310L. doi:10.1063/1.4824828.
197. ^ Bourzac, Katherine. "Superfast, Bendable Electronic Switches Made from Graphene | MIT Technology Review". Technologyreview.com. Retrieved 2013-08-24.
198. ^ Ekiz, O.O., et al. (2011). "Reversible Electrical Reduction and Oxidation of Graphene Oxide". ACS Nano 5 (4): 2475–2482. doi:10.1021/nn1014215. PMID 21391707.
Ekiz, O.O., et al. (2011). "Supporting information for Reversible Electrical Reduction and Oxidation of Graphene Oxide". ACS Nano 5 (4): 2475–2482. doi:10.1021/nn1014215. PMID 21391707.
199. ^ Wang, X.; et al. (2007). "Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells". Nano Letters 8 (1): 323–7. Bibcode:2008NanoL...8..323W. doi:10.1021/nl072838r. PMID 18069877.
200. ^ Eda G, Fanchini G, Chhowalla M (2008). "Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material". Nat Nanotechnol 3 (5): 270–4. doi:10.1038/nnano.2008.83. PMID 18654522.
201. ^ Wang, Yu et al. (2009). "Large area, continuous, few-layered graphene as anodes in organic photovoltaic devices". Applied Physics Letters 95 (6): 063302. Bibcode:2009ApPhL..95f3302W. doi:10.1063/1.3204698.
202. ^ Wu, J.B.; et al. (2010). "Organic Light-Emitting Diodes on Solution-Processed Graphene Transparent Electrodes". ACS Nano 4: 43. doi:10.1021/nn900728d.
203. ^ Matyba, P.; et al. (2010). "Graphene and Mobile Ions: The Key to All-Plastic, Solution-Processed Light-Emitting Devices". ACS Nano 4 (2): 637–42. doi:10.1021/nn9018569. PMID 20131906.
204. ^ Waugh, Rob. "Hi-tech 'wonder material' graphene has an unexpected use – it can distill vodka at room temperature". Daily Mail (London).
205. ^ Cohen-Tanugi, David; Grossman, Jeffrey C. (2012). "Water Desalination across Nanoporous Graphene". Nano Letters 12 (7): 3602–3608. Bibcode:2012NanoL..12.3602C. doi:10.1021/nl3012853. ISSN 1530-6984. PMID 22668008.
206. ^ a b c Mukhopadhyay, Prithu (2013). Graphite, Graphene and their Polymer Nanocomposites. Boca Raton, Florida: Taylor & Francis Group. pp. 202–213. ISBN 978-1-4398-2779-6.
207. ^ "Graphene-based solar cell hits record 15.6 percent efficiency". Gizmag.com. Retrieved 2014-01-23.
208. ^ Wang, J. T. W.; Ball, J. M.; Barea, E. M.; Abate, A.; Alexander-Webber, J. A.; Huang, J.; Saliba, M.; Mora-Sero, I. N.; Bisquert, J.; Snaith, H. J.; Nicolas, R. J. (2013). "Low-temperature processed electron collection layers of Graphene/TiO2 nanocomposites in thin film perovskite solar cells". Nano Letters: 131216131814005. doi:10.1021/nl403997a.
209. ^ "Graphene organic photovoltaics: Flexible material only a few atoms thick may offer cheap solar power". ScienceDaily. July 24, 2010.
Walker, Sohia. (2010-08-04) Use of graphene photovoltaics as alternate source of energy|Computer Talks. Comptalks.com. Retrieved on 2010-12-10.
210. ^ inhabitat.com cooperating with ICFO (Institute of Photonic Sciences)(2013-04-03
211. ^ Dan, Yaping; Lu, Ye; Kybert, Nicholas J.; Luo, Zhengtang; Johnson, A. T. Charlie (April 2009). "Intrinsic Response of Graphene Vapor Sensors". Nano Letters 9 (4): 1472–1475. arXiv:0811.3091. Bibcode:2009NanoL...9.1472D. doi:10.1021/nl8033637. PMID 19267449.
212. ^ Nihar Mohanty, David Moore, Zhiping Xu, T. S. Sreeprasad, Ashvin Nagaraja, Alfredo A. Rodriguez and Vikas Berry (2012). "Nanotomy Based Production of Transferrable and Dispersible Graphene-Nanostructures of Controlled Shape and Size". Nature Communications 3 (5): 844. Bibcode:2012NatCo...3E.844M. doi:10.1038/ncomms1834.
213. ^ Jinming Cai, Pascal Ruffieux, Rached Jaafar, Marco Bieri, Thomas Braun, Stephan Blankenburg, Matthias Muoth, Ari P. Seitsonen, Moussa Saleh, Xinliang Feng, Klaus Müllen & Roman Fasel (2010). "Atomically precise bottom-up fabrication of graphene nanoribbons". Nature 466 (7305): 470. Bibcode:2010Natur.466..470C. doi:10.1038/nature09211.
214. ^ Wang, Z. F., Shi, Q. W., Li, Q., Wang, X., Hou, J. G., Zheng, H., et al. (2007). "Z-shaped graphene nanoribbon quantum dot device". Applied Physics Letters 91 (5): 053109. arXiv:0705.0023. Bibcode:2007ApPhL..91e3109W. doi:10.1063/1.2761266.
215. ^ Wang, H.; Nezich, D.; Kong, J.; Palacios, T. (2009). "Graphene Frequency Multipliers". IEEE Electr. Device. L. 30 (5): 547. doi:10.1109/LED.2009.2016443. Lay summary.
D. Cricchio, P. P. Corso, E. Fiordilino, G. Orlando, and F. Persico (2009). "A paradigm of fullerene". J. Phys. B 42 (8): 085404. Bibcode:2009JPhB...42h5404C. doi:10.1088/0953-4075/42/8/085404.
216. ^ Liu, Ming; Yin, Xiaobo, Ulin-Avila, Erick, Geng, Baisong, Zentgraf, Thomas, Ju, Long, Wang, Feng, Zhang, Xiang (8 May 2011). "A graphene-based broadband optical modulator". Nature 474 (7349): 64–67. Bibcode:2011Natur.474...64L. doi:10.1038/nature10067. PMID 21552277.
217. ^ Yu, W.; Xie, H.; Wang, X.; Wang, X. (2011). "Significant thermal conductivity enhancement for nanofluids containing graphene nanosheets". Physics Letters A 375 (10): 1323. doi:10.1016/j.physleta.2011.01.040.
218. ^ R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, A. K. Geim (2008). "Fine Structure Constant Defines Visual Transparency of Graphene". Science 320 (5881): 1308. Bibcode:2008Sci...320.1308N. doi:10.1126/science.1156965. PMID 18388259.
219. ^ S. Eigler (2009). "A new parameter based on graphene for characterizing transparent, conductive materials". Carbon 47 (12): 2936–2939. doi:10.1016/j.carbon.2009.06.047.
220. ^ Stoller, Meryl D.; Sungjin Park, Yanwu Zhu, Jinho An, and Rodney S. Ruoff (2008). "Graphene-Based Ultracapacitors" (PDF). Nano Lett 8 (10): 3498–502. Bibcode:2008NanoL...8.3498S. doi:10.1021/nl802558y. PMID 18788793.
221. ^ Malasarn, Davin (2013-02-19). "UCLA researchers develop new technique to scale up production of graphene micro-supercapacitors / UCLA Newsroom". Newsroom.ucla.edu. Retrieved 2013-05-02.
222. ^ David, L.; Bhandavat, R.; Kulkarni, G.; Pahwa, S.; Zhong, Z.; Singh, G. (2013). "Synthesis of Graphene Films by Rapid Heating and Quenching at Ambient Pressures and Their Electrochemical Characterization". ACS Applied Materials & Interfaces 5 (3): 546. doi:10.1021/am301782h.
"Fabrication and Electrochemical Characterization of Single and Multi-Layer Graphene Anodes for Lithium-Ion Batteries". Jes.ecsdl.org. Retrieved 2013-06-24.
223. ^ Yao, F.; Güneş, F.; Ta, H. Q.; Lee, S. M.; Chae, S. J.; Sheem, K. Y.; Cojocaru, C. S.; Xie, S. S.; Lee, Y. H. (2012). "Diffusion Mechanism of Lithium Ion through Basal Plane of Layered Graphene". Journal of the American Chemical Society 134 (20): 8646–8654. doi:10.1021/ja301586m. PMID 22545779.
224. ^ Johnson, Dexter (2013-01-17). "Faster and Cheaper Process for Graphene in Li-ion Batteries - IEEE Spectrum". Spectrum.ieee.org. Retrieved 2013-06-24.
225. ^ Johnson, Dexter (2012-03-21). "Graphene-Silicon Anodes for Li-ion Batteries Go Commercial - IEEE Spectrum". Spectrum.ieee.org. Retrieved 2014-02-26.
226. ^ "XGS presents new silicon-graphene anode materials for lithium-ion batteries". Phys.org. Retrieved 2014-02-26.
227. ^ "Straintronics: Stanford engineers create piezoelectric graphene". Stanford University. Retrieved 16 April 2012.
Ong, M.; Reed, E.J. (2012). "Engineered Piezoelectricity in Graphene". ACS Nano 6 (2): 1387–94. doi:10.1021/nn204198g. PMID 22196055.
228. ^ Mohanty, Nihar; Vikas Berry (2008). "Graphene-based Single-Bacterium Resolution Biodevice and DNA-Transistor – Interfacing Graphene-Derivatives with Nano and Micro Scale Biocomponents". Nano Letters 8 (12): 4469–76. Bibcode:2008NanoL...8.4469M. doi:10.1021/nl802412n. PMID 18983201.
229. ^ Xu, M. S. Xu; D. Fujita and N. Hanagata (2009). "Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies". Small 5 (23): 2638–49. doi:10.1002/smll.200900976. PMID 19904762.
230. ^ "Bill Gates condom challenge 'to be met' by graphene scientists". BBC News. 20 November 2013. Retrieved 21 November 2013.
231. ^ "Graphene found to efficiently absorb radio waves". KurzweilAI. Retrieved 2014-02-26.
232. ^ Wu, B.; Tuncer, H. M.; Naeem, M.; Yang, B.; Cole, M. T.; Milne, W. I.; Hao, Y. (2014). "Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz". Scientific Reports 4. doi:10.1038/srep04130.
233. ^ Wallace, P. R. (1947). "The Band Theory of Graphite". Physical Review 71 (9): 622. Bibcode:1947PhRv...71..622W. doi:10.1103/PhysRev.71.622.
234. ^ Lamas, C.A.; D. C. Cabra, and N. Grandi (2009). "Generalized Pomeranchuk instabilities in graphene". Physical Review B 80 (7). arXiv:0812.4406. Bibcode:2009PhRvB..80g5108L. doi:10.1103/PhysRevB.80.075108.