Two-dimensional gas of massless Dirac fermions in graphene

n-Type behavior of graphene supported on Si/SiO(2) substrates

Results are presented from an experimental and theoretical study of the electronic properties of back-gated graphene field effect transistors (FETs) on Si/SiO(2) substrates. The excess charge on the graphene was observed by sweeping the gate voltage to determine the charge neutrality point in the graphene. Devices exposed to laboratory environment for several days were always found to be initially p-type. After approximately 20 h at 200 degrees C in approximately 5 x 10(-7) Torr vacuum, the FET slowly evolved to n-type behavior with a final excess electron density on the graphene of approximately 4 x 10(12) e/cm(2). This value is in excellent agreement with our theoretical calculations on SiO(2), where we have used molecular dynamics to build the SiO(2) structure and then density functional theory to compute the electronic structure. The essential theoretical result is that the SiO(2) has a significant surface state density just below the conduction band edge that donates electrons to the graphene to balance the chemical potential at the interface. An electrostatic model for the FET is also presented that produces an expression for the gate bias dependence of the carrier density.

Unconventional quasiparticle lifetime in graphene

We address the question of how large can the lifetime of electronic states be at low energies in graphene, below the scale of the optical phonon modes. For this purpose, we study the many-body effects at the K point of the spectrum, which induce a strong coupling between electron-hole pairs and out-of-plane phonons. We show the existence of a soft branch of hybrid states below the electron-hole continuum when graphene is close to the charge neutrality point, leading to an inverse lifetime proportional to the cube of the quasiparticle energy. This implies that a crossover should be observed in transport properties, from such a slow decay rate to the lower bound given at very low energies by the decay into acoustic phonons.

Disorder-induced enhancement of transport through graphene p-n junctions

We investigate the electron transport through a graphene p-n junction under a perpendicular magnetic field. By using the Landauer-Büttiker formalism combined with the nonequilibrium Green function method, the conductance is studied for clean and disordered samples. For the clean p-n junction, the conductance is quite small. In the presence of disorders, it is strongly enhanced and exhibits a plateau structure at a suitable range of disorders. Our numerical results show that the lowest plateau can survive for a very broad range of disorder strength, but the existence of high plateaus depends on system parameters and sometimes cannot be formed at all. When the disorder is slightly outside of this disorder range, some conductance plateaus can still emerge with its value lower than the ideal value. These results are in excellent agreement with a recent experiment.

Electronic and magnetic properties of quasifreestanding graphene on Ni

For the purpose of recovering the intriguing electronic properties of freestanding graphene at a solid surface, graphene self-organized on a Au monolayer on Ni(111) is prepared and characterized by scanning tunneling microscopy. Angle-resolved photoemission reveals a gapless linear pi-band dispersion near K[over] as a fingerprint of strictly monolayer graphene and a Dirac crossing energy equal to the Fermi energy (EF) within 25 meV meaning charge neutrality. Spin resolution shows a Rashba effect on the pi states with a large (approximately 13 meV) spin-orbit splitting up to EF which is independent of k.

Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy

We investigate the ultrafast relaxation dynamics of hot Dirac fermionic quasiparticles in multilayer epitaxial graphene using ultrafast optical differential transmission spectroscopy. We observe differential transmission spectra which are well described by interband transitions with no electron-hole interaction. Following the initial thermalization and emission of high-energy phonons, the electron cooling is determined by electron-acoustic phonon scattering, found to occur on the time scale of 1 ps for highly doped layers, and 4-11 ps in undoped layers. The spectra also provide strong evidence for the multilayer structure and doping profile of thermally grown epitaxial graphene on SiC.

Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering

We reduce the dimensionless interaction strength alpha in graphene by adding a water overlayer in ultrahigh vacuum, thereby increasing dielectric screening. The mobility limited by long-range impurity scattering is increased over 30%, due to the background dielectric constant enhancement leading to a reduced interaction of electrons with charged impurities. However, the carrier-density-independent conductivity due to short-range impurities is decreased by almost 40%, due to reduced screening of the impurity potential by conduction electrons. The minimum conductivity is nearly unchanged, due to canceling contributions from the electron-hole puddle density and long-range impurity mobility. Experimental data are compared with theoretical predictions with excellent agreement.

Electric property evolution of structurally defected multilayer graphene

We report on the influence of structural disorder on the electrical properties of multilayer graphene (MLG). Exponential decreases in the conductance and transconductance with increase of defects in the MLG were observed, which could be explained by the percolation and the variable range hopping conduction. An enhancement of p-type nature with increasing disorders was considered to be the result of oxygen doping in the graphene sheets introduced by oxygen plasma. The rapid increase of low-frequency noise was attributed to the formation of conductive network through the continuum percolation, as the low-frequency noise could be increased by the enhanced carrier scattering at the defect sites. We hope that our result should suggest a simple method of tuning the electrical properties of graphene.

Graphene-based atomic-scale switches

Graphene's remarkable mechanical and electrical properties, combined with its compatibility with existing planar silicon-based technology, make it an attractive material for novel computing devices. We report the development of a nonvolatile memory element based on graphene break junctions. Our devices have demonstrated thousands of writing cycles and long retention times. We propose a model for device operation based on the formation and breaking of carbon atomic chains that bridge the junctions. We demonstrate information storage based on the concept of rank coding, in which information is stored in the relative conductance of graphene switches in a memory cell.

Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects

Graphene is a recently discovered carbon-based material with unique physical properties. This is a monolayer of graphite, and the two-dimensional electrons and holes in it are described by the effective Dirac equation with a vanishing effective mass. As a consequence, the electromagnetic response of graphene is predicted to be strongly nonlinear. We develop a quasi-classical kinetic theory of the nonlinear electromagnetic response of graphene, taking into account the self-consistent-field effects. The response of the system to both harmonic and pulse excitation is considered. The frequency multiplication effect, resulting from the nonlinearity of the electromagnetic response, is studied under realistic experimental conditions. The frequency upconversion efficiency is analyzed as a function of the applied electric field and parameters of the samples. Possible applications of graphene in terahertz electronics are discussed.

Magnetoresistance of nanoscale molecular devices based on Aharonov-Bohm interferometry

Control of conductance in molecular junctions is of key importance in the growing field of molecular electronics. The current in these junctions is often controlled by an electric gate designed to shift conductance peaks into the low bias regime. Magnetic fields, on the other hand, have rarely been used due to the small magnetic flux captured by molecular conductors (an exception is the Kondo effect in single-molecule transistors). This is in contrast to a related field, electronic transport through mesoscopic devices, where considerable activity with magnetic fields has led to a rich description of transport. The scarcity of experimental activity is due to the belief that significant magnetic response is obtained only when the magnetic flux is of the order of the quantum flux, while attaining such a flux for molecular and nanoscale devices requires unrealistic magnetic fields. Here we review recent theoretical work regarding the essential physical requirements necessary for the construction of nanometer-scale magnetoresistance devices based on an Aharonov-Bohm molecular interferometer. We show that control of the conductance properties using small fractions of a magnetic flux can be achieved by carefully adjusting the lifetime of the conducting electrons through a pre-selected single state that is well separated from other states due to quantum confinement effects. Using a simple analytical model and more elaborate atomistic calculations we demonstrate that magnetic fields which give rise to a magnetic flux comparable to 10(-3) of the quantum flux can be used to switch a class of different molecular and nanometer rings, ranging from quantum corrals, carbon nanotubes and even a molecular ring composed of polyconjugated aromatic materials. The unique characteristics of the magnetic field as a gate is further discussed and demonstrated in two different directions. First, a three-terminal molecular router devices that can function as a parallel logic gate, processing two logic operations simultaneously, is presented. Second, the role of inelastic effects arising from electron-phonon couplings on the magnetoresistance properties is analyzed. We show that a remarkable difference between electric and magnetic gating is also revealed when inelastic effects become significant. The inelastic broadening of response curves to electric gates is replaced by a narrowing of magnetoconductance peaks, thereby enhancing the sensitivity of the device.

Weak localization of Dirac fermions in graphene

In the presence of the charged impurities, we study the weak localization effect by evaluating the quantum interference correction to the conductivity of Dirac fermions in graphene. With the inelastic scattering rate due to electron-electron interactions obtained from our previous work, we investigate the dependence of the quantum interference correction on the carrier concentration, the temperature, the magnetic field, and the size of the sample. It is found that weak localization is present in large size samples at finite carrier doping. Its strength becomes weakened or quenched when the sample size is less than a few microns at low temperatures as studied in the experiments. In the region close to zero doping, the system may become delocalized. The minimum conductivity at low temperature for experimental sample sizes is found to be close to the data.

New generation of massless Dirac fermions in graphene under external periodic potentials

We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.

Quenching of the quantum Hall effect in multilayered epitaxial graphene: the role of undoped planes

We propose a mechanism for the quenching of the Shubnikov-de Haas oscillations and the quantum Hall effect observed in epitaxial graphene. Experimental data show that the scattering time of the conduction electron is magnetic field dependent and of the order of the cyclotron orbit period, i.e., it can be much smaller than the zero field scattering time. Our scenario involves the extraordinary graphene n=0 Landau level of the uncharged layers which is pinned at the Fermi level. We find that the coupling between this n=0 Landau level and the conducting states of the doped plane leads to a scattering mechanism having the right magnitude to explain the experimental data.

Depositing graphene films on solid and perforated substrates

Graphene-a monolayer of graphite-has attracted vast interest recently owing to its perfect two-dimensional crystallographic nature and its potential use in a new generation of microelectronic devices. Yet, a deposition method, which results in a large coverage of monolayer thick graphite, is still lacking. By using a chemical mechanical polishing (CMP) method we were able to deposit stress-free graphene on solid and perforated substrates alike, achieving area coverage of hundreds of microns squared.

Electron spin resonance signal of Luttinger liquids and single-wall carbon nanotubes

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid state of correlated metals is presented. The ESR measurables such as the signal intensity and the linewidth are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line broadening which is related to the spin-symmetry breaking and the electron-electron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the noninteracting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions.

Superconducting switch made of graphene-nanoribbon junctions

The transmission of superconductor-graphene nanoribbon-superconductor junctions (SGS) has been studied by the non-equilibrium Green's function method. It is found that the on-site potential U in the center zigzag graphene nanoribbon (ZGNR) of the SGS junction plays an important role in the magnitude of the supercurrent I(c). As the effective Fermi energy μ(eff) (μ(eff) = μ(F)-U) goes from negative to positive, the SGS junction would suddenly transform from an 'OFF' state to an 'ON' state. And, as μ(eff) increases further, the I(c) will continue to increase. This switching behavior of the SGS junction shares the same origin with the zigzag GNR valley-isospin valve (Rycerz et al 2007 Nat. Phys. 3 172). Besides the valley-isospin, the density of states will also have an effect on the suppression of I(c).

Electron beam supercollimation in graphene superlattices

Although electrons and photons are intrinsically different, importing useful concepts in optics to electronics performing similar functions has been actively pursued over the last two decades. In particular, collimation of an electron beam is a long-standing goal. We show that ballistic propagation of an electron beam with virtual no spatial spreading or diffraction, without a waveguide or external magnetic field, can be achieved in graphene under an appropriate class of experimentally feasible one-dimensional external periodic potentials. The novel chiral quasi-one-dimensional metallic state that the charge carriers are in originates from a collapse of the intrinsic helical nature of the charge carriers in graphene owing to the superlattice potential. Beyond providing a new way to constructing chiral one-dimensional states in two dimensions, our findings should be useful in graphene-based electronic devices (e.g., for information processing) utilizing some of the highly developed concepts in optics.

Highly conducting graphene sheets and Langmuir-Blodgett films

Graphene is an intriguing material with properties that are distinct from those of other graphitic systems. The first samples of pristine graphene were obtained by 'peeling off' and epitaxial growth. Recently, the chemical reduction of graphite oxide was used to produce covalently functionalized single-layer graphene oxide. However, chemical approaches for the large-scale production of highly conducting graphene sheets remain elusive. Here, we report that the exfoliation-reintercalation-expansion of graphite can produce high-quality single-layer graphene sheets stably suspended in organic solvents. The graphene sheets exhibit high electrical conductance at room and cryogenic temperatures. Large amounts of graphene sheets in organic solvents are made into large transparent conducting films by Langmuir-Blodgett assembly in a layer-by-layer manner. The chemically derived, high-quality graphene sheets could lead to future scalable graphene devices.

Classical and quantum routes to linear magnetoresistance

The hallmark of materials science is the ability to tailor the microstructure of a given material to provide a desired response. Carbon mixed with iron provides the steel of buildings and bridges; impurities sprinkled in silicon single crystals form the raw materials of the electronics revolution; pinning centres in superconductors let them become powerful magnets. Here, we show that either adding a few parts per million of the proper chemical impurities to indium antimonide, a well-known semiconductor, or redesigning the material's structure on the micrometre scale, can transform its response to an applied magnetic field. The former approach is purely quantum mechanical; the latter a classical outgrowth of disorder, turned to advantage. In both cases, the magnetoresistive response--at the heart of magnetic sensor technology--can be converted to a simple, large and linear function of field that does not saturate. Harnessing the effects of disorder has the further advantage of extending the useful applications range of such a magnetic sensor to very high temperatures by circumventing the usual limitations imposed by phonon scattering.

High-yield production of graphene by liquid-phase exfoliation of graphite

Fully exploiting the properties of graphene will require a method for the mass production of this remarkable material. Two main routes are possible: large-scale growth or large-scale exfoliation. Here, we demonstrate graphene dispersions with concentrations up to approximately 0.01 mg ml(-1), produced by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone. This is possible because the energy required to exfoliate graphene is balanced by the solvent-graphene interaction for solvents whose surface energies match that of graphene. We confirm the presence of individual graphene sheets by Raman spectroscopy, transmission electron microscopy and electron diffraction. Our method results in a monolayer yield of approximately 1 wt%, which could potentially be improved to 7-12 wt% with further processing. The absence of defects or oxides is confirmed by X-ray photoelectron, infrared and Raman spectroscopies. We are able to produce semi-transparent conducting films and conducting composites. Solution processing of graphene opens up a range of potential large-area applications, from device and sensor fabrication to liquid-phase chemistry.

Domain walls in gapped graphene

The electronic properties of a particular class of domain walls in gapped graphene are investigated. We show that they can support midgap states which are localized in the vicinity of the domain wall and propagate along its length. With a finite density of domain walls, these states can alter the electronic properties of gapped graphene significantly. If the midgap band is partially filled, the domain wall can behave like a one-dimensional metal embedded in a semiconductor and could potentially be used as a single-channel quantum wire.

Bridge between Abelian and non-Abelian fractional quantum Hall states

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that K-component Halperin wave functions may be a common basis for both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

Near-edge x-ray absorption fine-structure investigation of graphene

We report the near-edge x-ray absorption fine-structure (NEXAFS) spectrum of a single layer of graphite (graphene) obtained by micromechanical cleavage of highly ordered pyrolytic graphite on a SiO2 substrate. We utilized a photoemission electron microscope to separately study single-, double-, and few-layers graphene samples. In single-layer graphene we observe a splitting of the pi resonance and a clear signature of the predicted interlayer state. The NEXAFS data illustrate the rapid evolution of the electronic structure with the increased number of layers.

Phase transitions of Dirac electrons in bismuth

The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple flavors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy.

Contact and edge effects in graphene devices

Electrical transport studies on graphene have been focused mainly on the linear dispersion region around the Fermi level and, in particular, on the effects associated with the quasiparticles in graphene behaving as relativistic particles known as Dirac fermions. However, some theoretical work has suggested that several features of electron transport in graphene are better described by conventional semiconductor physics. Here we use scanning photocurrent microscopy to explore the impact of electrical contacts and sheet edges on charge transport through graphene devices. The photocurrent distribution reveals the presence of potential steps that act as transport barriers at the metal contacts. Modulations in the electrical potential within the graphene sheets are also observed. Moreover, we find that the transition from the p- to n-type regime induced by electrostatic gating does not occur homogeneously within the sheets. Instead, at low carrier densities we observe the formation of p-type conducting edges surrounding a central n-type channel.

Strong suppression of electrical noise in bilayer graphene nanodevices

Low-frequency 1/f noise is ubiquitous and dominates the signal-to-noise performance in nanodevices. Here we investigate the noise characteristics of single-layer and bilayer graphene nanodevices and uncover an unexpected 1/f noise behavior for bilayer devices. Graphene is a single layer of graphite, where carbon atoms form a two-dimensional (2D) honeycomb lattice. Despite the similar composition, bilayer graphene (two graphene monolayers stacked in the natural graphite order) is a distinct 2D system with a different band structure and electrical properties. 1,2In graphene monolayers, the 1/f noise is found to follow Hooge's empirical relation with a noise parameter comparable to that of bulk semiconductors. However, this 1/f noise is strongly suppressed in bilayer graphene devices and exhibits an unusual dependence on the carrier density, different from most other materials. The unexpected noise behavior in graphene bilayers is associated with its unique band structure that varies with the charge distribution among the two layers, resulting in an effective screening of potential fluctuations due to external impurity charges. The findings here point to exciting opportunities for graphene bilayers in low-noise applications.

Approaching ballistic transport in suspended graphene

The discovery of graphene raises the prospect of a new class of nanoelectronic devices based on the extraordinary physical properties of this one-atom-thick layer of carbon. Unlike two-dimensional electron layers in semiconductors, where the charge carriers become immobile at low densities, the carrier mobility in graphene can remain high, even when their density vanishes at the Dirac point. However, when the graphene sample is supported on an insulating substrate, potential fluctuations induce charge puddles that obscure the Dirac point physics. Here we show that the fluctuations are significantly reduced in suspended graphene samples and we report low-temperature mobility approaching 200,000 cm2 V-1 s-1 for carrier densities below 5 x 109 cm-2. Such values cannot be attained in semiconductors or non-suspended graphene. Moreover, unlike graphene samples supported by a substrate, the conductivity of suspended graphene at the Dirac point is strongly dependent on temperature and approaches ballistic values at liquid helium temperatures. At higher temperatures, above 100 K, we observe the onset of thermally induced long-range scattering.

sigma- and pi-defects at graphene nanoribbon edges: building spin filters

The presence of certain kinds of defects at the edges of monohydrogenated zigzag graphene nanoribbons changes dramatically the charge transport properties inducing a spin-polarized conductance. Using an approach based on density functional theory and nonequilibrium Green's function formalism to calculate the transmittance, we classify the defects in different classes depending on their distinct transport properties: (i) sigma-defects, which do not affect the transmittance close to the Fermi energy (EF); and (ii) pi-defects, which cause a spin polarization of the transmittance and that can be further divided into either electron or hole defects if the spin transport polarization results in larger transmittance for the up or down spin channel, respectively.

Synthesis of few-layer graphene via microwave plasma-enhanced chemical vapour deposition

If graphene is ever going to live up to the promises of future nanoelectronic devices, an easy and cheap route for mass production is an essential requirement. A way to extend the capabilities of plasma-enhanced chemical vapour deposition to the synthesis of freestanding few-layer graphene is presented. Micrometre-wide flakes consisting of four to six atomic layers of stacked graphene sheets have been synthesized by controlled recombination of carbon radicals in a microwave plasma. A simple and highly reproducible technique is essential, since the resulting flakes can be synthesized without the need for a catalyst on the surface of any substrate that withstands elevated temperatures up to 700 °C. A thorough structural analysis of the flakes is performed with electron microscopy, x-ray diffraction, Raman spectroscopy and scanning tunnelling microscopy. The resulting graphene flakes are aligned vertically to the substrate surface and grow according to a three-step process, as revealed by the combined analysis of electron microscopy and x-ray photoelectron spectroscopy.

Electronic and magnetic properties of armchair and zigzag graphene nanoribbons

The electronic properties, band gap, and ionization potential of zigzag and armchair graphene nanoribbons are calculated as a function of the number of carbon atoms in the ribbon employing density functional theory at the B3LYP6-31G* level. In armchair ribbons, the ionization potential and band gap show a gradual decrease with length. For zigzag ribbons, the dependence of the band gap and ionization potential on ribbon length is different depending on whether the ribbon has an unpaired electron or not. It is also found that boron and nitrogen zigzag and armchair doped graphene nanoribbons have a triplet ground state and could be ferromagnetic.

Anisotropic spin relaxation in graphene

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.

Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance sigma_{xy} and the longitudinal conductance sigma_{xx} are computed. We demonstrate that bond disorder can produce a plateaulike feature centered at nu=0, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between +/-E_{c}, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be 2.47+/-0.04. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between approximately 1.0 and approximately 7/3.

Localized magnetic states in graphene

We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level, lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.

Doping graphene with metal contacts

Making devices with graphene necessarily involves making contacts with metals. We use density functional theory to study how graphene is doped by adsorption on metal substrates and find that weak bonding on Al, Ag, Cu, Au, and Pt, while preserving its unique electronic structure, can still shift the Fermi level with respect to the conical point by approximately 0.5 eV. At equilibrium separations, the crossover from p-type to n-type doping occurs for a metal work function of approximately 5.4 eV, a value much larger than the graphene work function of 4.5 eV. The numerical results for the Fermi level shift in graphene are described very well by a simple analytical model which characterizes the metal solely in terms of its work function, greatly extending their applicability.

The effects of electronic field on the atomic structure of the graphene/α-SiO(2) interface

The atomic structure of the graphene/α-SiO(2)(0001) interface under electric field F with different intensities is studied using the density functional theory method. Simulation results indicate that the atomic structure of the graphene/α-SiO(2)(0001) interface has only a slight change under the condition of F≤0.02 au. However, the distance between substrate and graphene d(0) changes evidently. Moreover, as F reaches 0.03 au, the formation of a C-O covalent bond on the interface is present, which would destroy the excellent electronic properties of graphene. Thus, there exists a maximum for F in application of the graphene.

Proposal for a graphene-based current nanoswitch

We propose a graphene-based model nanoswitch for the control of current flow. The device is made up of a graphene nanoribbon with a longitudinal semi-infinite septum on its left side. The septum defines two terminals, where the current can be selectively directed by means of a high magnetic field and an adjustable potential step induced by a top gate. The device's working mechanism is based on the spatial chirality of currents in high magnetic fields and on the possibility of determining the electron-like or hole-like nature of the particles involved in transport by means of the adjustable potential step. The role of critical parameters such as the width of the ribbon and the presence of disorder are discussed.