Two-dimensional gas of massless Dirac fermions in 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.

Substrate-free gas-phase synthesis of graphene sheets

We present a novel method for synthesizing graphene sheets in the gas phase using a substrate-free, atmospheric-pressure microwave plasma reactor. Graphene sheets were synthesized by passing liquid ethanol droplets into an argon plasma. The graphene sheets were characterized by transmission electron microscopy, electron energy loss spectroscopy, Raman spectroscopy, and electron diffraction. We prove that graphene can be created without three-dimensional materials or substrates and demonstrate a possible avenue to the large-scale synthesis of graphene.

Prediction of very large values of magnetoresistance in a graphene nanoribbon device

Graphene has emerged as a versatile material with outstanding electronic properties that could prove useful in many device applications. Recently, the demonstration of spin injection into graphene and the observation of long spin relaxation times and lengths have suggested that graphene could play a role in 'spintronic' devices that manipulate electron spin rather than charge. In particular it has been found that zigzag graphene nanoribbons have magnetic (or spin) states at their edges, and that these states can be either antiparallel or parallel. Here we report the results of first-principles simulations that predict that spin-valve devices based on graphene nanoribbons will exhibit magnetoresistance values that are thousands of times higher than previously reported experimental values. These remarkable values can be linked to the unique symmetry of the band structure in the nanoribbons. We also show that it is possible to manipulate the band structure of the nanoribbons to generate highly spin-polarized currents.

Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography

The practical realization of nanoscale electronics faces two major challenges: the precise engineering of the building blocks and their assembly into functional circuits. In spite of the exceptional electronic properties of carbon nanotubes, only basic demonstration devices have been realized that require time-consuming processes. This is mainly due to a lack of selective growth and reliable assembly processes for nanotubes. However, graphene offers an attractive alternative. Here we report the patterning of graphene nanoribbons and bent junctions with nanometre-precision, well-defined widths and predetermined crystallographic orientations, allowing us to fully engineer their electronic structure using scanning tunnelling microscope lithography. The atomic structure and electronic properties of the ribbons have been investigated by scanning tunnelling microscopy and tunnelling spectroscopy measurements. Opening of confinement gaps up to 0.5 eV, enabling room-temperature operation of graphene nanoribbon-based devices, is reported. This method avoids the difficulties of assembling nanoscale components and may prove useful in the realization of complete integrated circuits, operating as room-temperature ballistic electronic devices.

Graphene oxidation: thickness-dependent etching and strong chemical doping

Patterned graphene shows substantial potential for applications in future molecular-scale integrated electronics. Environmental effects are a critical issue in a single-layer material where every atom is on the surface. Especially intriguing is the variety of rich chemical interactions shown by molecular oxygen with aromatic molecules. We find that O 2 etching kinetics vary strongly with the number of graphene layers in the sample. Three-layer-thick samples show etching similar to bulk natural graphite. Single-layer graphene reacts faster and shows random etch pits in contrast to natural graphite where nucleation occurs at point defects. In addition, basal plane oxygen species strongly hole dope graphene, with a Fermi level shift of approximately 0.5 eV. These oxygen species desorb partially in an Ar gas flow, or under irradiation by far UV light, and readsorb again in an O 2 atmosphere at room temperature. This strongly doped graphene is very different from "graphene oxide" made by mineral acid attack.

Contact effects in graphene nanoribbon transistors

The effects of the various contact types and shapes on the performance of Schottky barrier graphene nanoribbon field-effect-transistors (GNRFETs) have been investigated using a real-space quantum transport simulator based on the NEGF approach self-consistently coupled to a three-dimensional Poisson solver for treating the electrostatics. The device channel considered is a double gate semiconducting armchair nanoribbon. The types of contacts considered are (a) a semi-infinite normal metal, (b) a semi-infinite graphene sheet, (c) finite size rectangular shape armchair graphene contacts, (d) finite size wedge shape graphene contacts, and (e) zigzag graphene nanoribbon contacts. Among these different contact types, the semi-infinite graphene sheet contacts show the worst performance because of their very low density of states around the Dirac point resulting in low transmission possibility through the Schottky barrier, both at ON and OFF states. Although all other types of contacts can have significant enhancement in I ON to I OFF ratio, the zigzag GNR contacts show promising and size invariant performance due to the metallic properties.

BCS Superconductivity of Dirac electrons in graphene layers

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.

Fully valley-polarized electron beams in graphene

We propose a device to break the valley degeneracy in graphene and produce fully valley-polarized currents that can be either split or collimated to a high degree in a experimentally controllable way. The proposal combines two recent seminal ideas: negative refraction and the concept of valleytronics in graphene. The key new ingredient lies in the use of the specular shape of the Fermi surface of the two valleys when a high electronic density is induced by a gate voltage (trigonal warping). By changing the gate voltage in a n-p-n junction of a graphene transistor, the device can be used as a valley beam splitter, where each of the beams belong to a different valley, or as a collimator. The result is demonstrated through an optical analogy with two-dimensional photonic crystals.

New magnetic field dependence of Landau levels in a graphenelike structure

We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field B as epsilon(n)(B) ~ [(n+gamma)B](2/3). This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value gamma=1/2 is found to result from the cancellation of a Berry phase.

Electronic spin drift in graphene field-effect transistors

We studied the drift of electron spins under an applied dc electric field in single layer graphene spin valves in a field-effect transport geometry at room temperature. In the metallic conduction regime (n approximately 3.5 x 10(16) m(-2)), for dc fields of about +/- 70 kV/m applied between the spin injector and spin detector, the spin valve signals are increased or decreased, depending on the direction of the dc field and the carrier type, by as much as +/- 50%. Sign reversal of the drift effect is observed when switching from hole to electron conduction. In the vicinity of the Dirac neutrality point the drift effect is strongly suppressed. The experiments are in quantitative agreement with a drift-diffusion model of spin transport.

A topological Dirac insulator in a quantum spin Hall phase

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields. Bulk Bi(1-x)Sb(x) single crystals are predicted to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi(1-x)Sb(x) is predicted to exhibit three-dimensional Dirac particles, another topic of heightened current interest following the new findings in two-dimensional graphene and charge quantum Hall fractionalization observed in pure bismuth. However, despite numerous transport and magnetic measurements on the Bi(1-x)Sb(x) family since the 1960s, no direct evidence of either topological Hall states or bulk Dirac particles has been found. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES), we report the direct observation of massive Dirac particles in the bulk of Bi(0.9)Sb(0.1), locate the Kramers points at the sample's boundary and provide a comprehensive mapping of the Dirac insulator's gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the 'topological metal'. They also suggest that this material has potential application in developing next-generation quantum computing devices that may incorporate 'light-like' bulk carriers and spin-textured surface currents.

Graphene-metal interface: two-terminal resistance of low-mobility graphene in high magnetic fields

The two-terminal magnetotransport of a single graphene layer was investigated up to a field of 55 T. The dependence of the electron transmission probability at the organo-metallic interface between the graphene and the metal electrodes was studied as a function of filling factor and electron density. A resistance-plateau spanning several tens of tesla width was observed. We argue that this plateau originates from an augmented sublattice spin-splitting due to the high surface-impurity concentration of the graphene layer. At electron densities close to the Dirac point, fingerprints of a thermally activated energy gap were observed.

Double and negative reflection of cold atoms in non-Abelian gauge potentials

Atom reflection is studied in the presence of a non-Abelian vector potential proportional to a spin-1/2 operator. The potential is produced by a relatively simple laser configuration for atoms with a tripod level scheme. We show that the atomic motion is described by two different dispersion branches with positive or negative chirality. As a consequence, atom reflection shows unusual features, since an incident wave may split into two reflected ones at a barrier, an ordinary specular reflection, and an additional nonspecular one. Remarkably, the latter wave can exhibit negative reflection and may become evanescent if the angle of incidence exceeds a critical value. These reflection properties are crucial for future designs in non-Abelian atom optics.

Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors

Sub-10 nm wide graphene nanoribbon field-effect transistors (GNRFETs) are studied systematically. All sub-10 nm GNRs afforded semiconducting FETs without exception, with Ion/Ioff ratio up to 10(6) and on-state current density as high as approximately 2000 microA/microm. We estimated carrier mobility approximately 200 cm2/V s and scattering mean free path approximately 10 nm in sub-10 nm GNRs. Scattering mechanisms by edges, acoustic phonon, and defects are discussed. The sub-10 nm GNRFETs are comparable to small diameter (d< or = approximately 1.2 nm) carbon nanotube FETs with Pd contacts in on-state current density and Ion/Ioff ratio, but have the advantage of producing all-semiconducting devices.

Role of symmetry in the transport properties of graphene nanoribbons under bias

The intrinsic transport properties of zigzag graphene nanoribbons (ZGNRs) are investigated using first-principles calculations. It is found that although all ZGNRs have similar metallic band structure, they show distinctly different transport behaviors under bias voltages, depending on whether they are mirror symmetric with respect to the midplane between two edges. Asymmetric ZGNRs behave as conventional conductors with linear current-voltage dependence, while symmetric ZGNRs exhibit unexpected very small currents with the presence of a conductance gap around the Fermi level. This difference is revealed to arise from different coupling between the conducting subbands around the Fermi level, which is dependent on the symmetry of the systems.

Zero-energy state in graphene in a high magnetic field

The fate of the charge-neutral Dirac point in graphene in a high magnetic field H has been investigated at low temperatures (T approximately 0.3 K). In samples with small gate-voltage offset V0, the resistance R0 at the Dirac point diverges steeply with H, signaling a crossover to a state with a very large R0. The approach to this state is highly unusual. Despite the steep divergence in R0, the profile of R0 vs T in fixed H saturates to a T-independent value below 2 K, consistent with gapless charge-carrying excitations.

Nanoengineering defect structures on graphene

We present a new way of nanoengineering graphene by using defect domains. These regions have ring structures that depart from the usual honeycomb lattice, though each carbon atom still has three nearest neighbors. A set of stable domain structures is identified by using density functional theory, including blisters, ridges, ribbons, and metacrystals. All such structures are made solely out of carbon; the smallest encompasses just 16 atoms. Blisters, ridges, and metacrystals rise up out of the sheet, while ribbons remain flat. In the vicinity of vacancies, the reaction barriers to formation are sufficiently low that such defects could be synthesized through the thermally activated restructuring of coalesced adatoms.

Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field

We show that the recently discovered double-valley splitting of the Landau levels in the quantum Hall effect in graphene can be explained as the perturbative orbital interaction of intravalley and intervalley microscopic orbital currents with a magnetic field. This effect is facilitated by the translationally noninvariant terms that correspond to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac fermions in quantum electrodynamics. We discuss recent data in view of these findings.

Origin of anomalous electronic structures of epitaxial graphene on silicon carbide

On the basis of first-principles calculations, we report that a novel interfacial atomic structure occurs between graphene and the surface of silicon carbide, destroying the Dirac point of graphene and opening a substantial energy gap there. In the calculated atomic structures, a quasiperiodic 6x6 domain pattern emerges out of a larger commensurate 6 sqrt [3] x 6 sqrt [3]R30 degrees periodic interfacial reconstruction, resolving a long standing experimental controversy on the periodicity of the interfacial superstructures. Our theoretical energy spectrum shows a gap and midgap states at the Dirac point of graphene, which are in excellent agreement with the recently observed anomalous angle-resolved photoemission spectra. Beyond solving unexplained issues in epitaxial graphene, our atomistic study may provide a way to engineer the energy gaps of graphene on substrates.

Epitaxial graphene on ruthenium

Graphene has been used to explore the fascinating electronic properties of ideal two-dimensional carbon, and shows great promise for quantum device architectures. The primary method for isolating graphene, micromechanical cleavage of graphite, is difficult to scale up for applications. Epitaxial growth is an attractive alternative, but achieving large graphene domains with uniform thickness remains a challenge, and substrate bonding may strongly affect the electronic properties of epitaxial graphene layers. Here, we show that epitaxy on Ru(0001) produces arrays of macroscopic single-crystalline graphene domains in a controlled, layer-by-layer fashion. Whereas the first graphene layer indeed interacts strongly with the metal substrate, the second layer is almost completely detached, shows weak electronic coupling to the metal, and hence retains the inherent electronic structure of graphene. Our findings demonstrate a route towards rational graphene synthesis on transition-metal templates for applications in electronics, sensing or catalysis.

Tunable stress and controlled thickness modification in graphene by annealing

Graphene has many unique properties which make it an attractive material for fundamental study as well as for potential applications. In this paper, we report the first experimental study of process-induced defects and stress in graphene using Raman spectroscopy and imaging. While defects lead to the observation of defect-related Raman bands, stress causes shift in phonon frequency. A compressive stress (as high as 2.1 GPa) was induced in graphene by depositing a 5 nm SiO(2) followed by annealing, whereas a tensile stress ( approximately 0.7 GPa) was obtained by depositing a thin silicon capping layer. In the former case, both the magnitude of the compressive stress and number of graphene layers can be controlled or modified by the annealing temperature. As both the stress and thickness affect the physical properties of graphene, this study may open up the possibility of utilizing thickness and stress engineering to improve the performance of graphene-based devices. Local heating techniques may be used to either induce the stress or reduce the thickness selectively.

Suppression of magnetotransport in strongly disordered graphene

A tight-binding model with randomly fluctuating atomic positions is studied to discuss the effect of strong disorder in graphene. We employ a strong-disorder expansion for the transport quantities and find a diffusive behavior, where the conductivity is decreasing with increasing disorder. For sufficiently strong disorder the magnetic field drops out of the diffusion coefficient and the conductivity. This signals a strong suppression of magnetotransport effects, a result which is consistent with recent experimental observations by Morozov et al.

Shot noise in graphene

We report measurements of current noise in single-layer and multilayer graphene devices. In four single-layer devices, including a p-n junction, the Fano factor remains constant to within +/-10% upon varying carrier type and density, and averages between 0.35 and 0.38. The Fano factor in a multilayer device is found to decrease from a maximal value of 0.33 at the charge-neutrality point to 0.25 at high carrier density. These results are compared to theories for shot noise in ballistic and disordered graphene.

Proposal for a new class of materials: spin gapless semiconductors

The concept of the spin gapless semiconductor in which both electron and hole can be fully spin polarized is proposed, and its possibility is presented on the basis of first-principles electronic structure calculations. Possible new physics and potential applications in spintronic devices based on the spin gapless semiconductors are discussed.

Hydrogen adsorption on boron doped graphene: an ab initio study

(i) The electronic and structural properties of boron doped graphene sheets, and (ii) the chemisorption processes of hydrogen adatoms on the boron doped graphene sheets have been examined by ab initio total energy calculations. In (i) we find that the structural deformations are very localized around the boron substitutional sites, and in accordance with previous studies (Endo et al 2001 J. Appl. Phys. 90 5670) there is an increase of the electronic density of states near the Fermi level. Our simulated scanning tunneling microscope (STM) images, for occupied states, indicate the formation of bright (triangular) spots lying on the substitutional boron (center) and nearest-neighbor carbon (edge) sites. Those STM images are attributed to the increase of the density of states within an energy interval of 0.5 eV below the Fermi level. For a boron concentration of ∼2.4%, we find that two boron atoms lying on the opposite sites of the same hexagonal ring (B1-B2 configuration) represents the energetically most stable configuration, which is in contrast with previous theoretical findings. Having determined the energetically most stable configuration for substitutional boron atoms on graphene sheets, we next considered the hydrogen adsorption process as a function of the boron concentration, (ii). Our calculated binding energies indicate that the C-H bonds are strengthened near boron substitutional sites. Indeed, the binding energy of hydrogen adatoms forming a dimer-like structure on the boron doped B1-B2 graphene sheet is higher than the binding energy of an isolated H(2) molecule. Since the formation of the H dimer-like structure may represent the initial stage of the hydrogen clustering process on graphene sheets, we can infer that the formation of H clusters is quite likely not only on clean graphene sheets, which is in consonance with previous studies (Hornekær et al 2006 Phys. Rev. Lett. 97 186102), but also on B1-B2 boron doped graphene sheets. However, for a low concentration of boron atoms, the formation of H dimer structures is not expected to occur near a single substitutional boron site. That is, the formation (or not) of H clusters on graphene sheets can be tuned by the concentration of substitutional boron atoms.

Dirac fermions at the H point of graphite: magnetotransmission studies

We report on far infrared magnetotransmission measurements on a thin graphite sample prepared by exfoliation of highly oriented pyrolytic graphite. In a magnetic field, absorption lines exhibiting a blueshift proportional to sqrt[B] are observed. This is a fingerprint for massless Dirac holes at the H point in bulk graphite. The Fermi velocity is found to be c[over ] =( 1.02+/-0.02) x 10(6) m/s and the pseudogap |Delta| at the H point is estimated to be below 10 meV. Although the holes behave to a first approximation as a strictly 2D gas of Dirac fermions, the full 3D band structure has to be taken into account to explain all the observed spectral features.

Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor

The recent discovery of graphene has led to many advances in two-dimensional physics and devices. The graphene devices fabricated so far have relied on SiO(2) back gating. Electrochemical top gating is widely used for polymer transistors, and has also been successfully applied to carbon nanotubes. Here we demonstrate a top-gated graphene transistor that is able to reach doping levels of up to 5x1013 cm-2, which is much higher than those previously reported. Such high doping levels are possible because the nanometre-thick Debye layer in the solid polymer electrolyte gate provides a much higher gate capacitance than the commonly used SiO(2) back gate, which is usually about 300 nm thick. In situ Raman measurements monitor the doping. The G peak stiffens and sharpens for both electron and hole doping, but the 2D peak shows a different response to holes and electrons. The ratio of the intensities of the G and 2D peaks shows a strong dependence on doping, making it a sensitive parameter to monitor the doping.

Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene

We show experimentally that multilayer graphene grown on the carbon terminated SiC(0001[over ]) surface contains rotational stacking faults related to the epitaxial condition at the graphene-SiC interface. Via first-principles calculation, we demonstrate that such faults produce an electronic structure indistinguishable from an isolated single graphene sheet in the vicinity of the Dirac point. This explains prior experimental results that showed single-layer electronic properties, even for epitaxial graphene films tens of layers thick.

Universal optical conductance of graphite

We find experimentally that the optical sheet conductance of graphite per graphene layer is very close to (pi/2)e2/h, which is the theoretically expected value of dynamical conductance of isolated monolayer graphene. Our calculations within the Slonczewski-Weiss-McClure model explain well why the interplane hopping leaves the conductance of graphene sheets in graphite almost unchanged for photon energies between 0.1 and 0.6 eV, even though it significantly affects the band structure on the same energy scale. The f-sum rule analysis shows that the large increase of the Drude spectral weight as a function of temperature is at the expense of the removed low-energy optical spectral weight of transitions between hole and electron bands.

Broken-symmetry states of Dirac fermions in graphene with a partially filled high Landau level

We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wave vectors +/-q*. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, which suggests an instability toward a charge density wave. A symmetry broken stripe phase is formed at large system size limit, which is robust against perturbation from disorder scattering. Such a quantum phase is experimentally observable through transport measurements. Associated with the special wave functions of the Dirac LL, both stripe and bubble phases become possible candidates for the ground state of the Dirac fermions in graphene with lower filling factors in the N=3 LL.

Density functional calculation of transition metal adatom adsorption on graphene

The functionalization of graphene (a single graphite layer) by the addition of transition metal atoms of Mn, Fe and Co to its surface has been investigated computationally using density functional theory. In the calculation, the graphene surface supercell was constructed from a single layer of graphite (0001) surface separated by vertical vacuum layers 2 nm thick. We found that the center of the hexagonal ring formed by carbon from graphene is the most stable site for Mn, Fe, Co to stay after optimization. The calculated spin-polarized band structures of the graphene encapsulating the Mn adatom indicate that the conduction bands are modified and move down due to the coupling between the Mn atom and graphene. For Fe adsorbed on the graphene surface, it is semi-half-metallic, and the spin polarization P is found to be 100%. The system of Co adatom on graphene exhibits metallic electronic structure due to the density of states (DOS) peak at the band center with both majority and minority spins. Local density of states analyses indicate a larger promotion of 4s electrons into the 3d state in Fe and Co, resulting in lower local moments compared to an Mn adatom on the graphite surface.

Origin of the complex molecular dynamics in functionalized discotic liquid crystals

The molecular dynamics of three dipole functionalized hexa-peri-hexabenzocoronenes have been studied using site-specific NMR techniques and dielectric spectroscopy as a function of temperature and pressure. These probes (i) suggest that the thermodynamic state completely controls the dynamic response, (ii) clarify the origin of two dynamic processes associated with the presence of two glass temperatures, and (iii) provide the first phase diagram for substances of this kind.

Electronic properties of nanotube-ribbon hybrid systems

In this work we use the tight-binding model to study the electronic properties of nanotube-ribbon hybrid systems. The nanotube-ribbon interactions will modify state energies, alter energy gaps, destroy state degeneracy, and create additional band-edge states. The bandstructures are asymmetric and symmetric about the Fermi energy when the interactions are turned on and off, respectively. The energy gap is found to vary sensitively with the nanotube location. Moreover, semiconductor-metal transition is predicted for nanotube-ribbon hybrid systems (I) and (III). For a zigzag ribbon, the partial flat bands at E(F) are almost unaffected by the nanotube-ribbon coupling although the bandstructures have been noticeably modified by such coupling; the energy gap of system (IV) is always zero. The effects of nanotube diameter and ribbon width on the energy gap and the density of states are also investigated. The semiconductor-metal transition can be accomplished by varying the nanotube location, the nanotube diameter or the ribbon width. The main features of the bandstructure are directly reflected in the density of states. The numbers, heights, and energies of the density of states peaks are strongly dependent on the nanotube-ribbon hoppings.

Determining the physisorption energies of molecules on graphene nanostructures by measuring the stochastic emission-current fluctuation

A method of determining the physisorption energy of molecules on carbon nanostructures using field emission current fluctuation measurements is presented. A stochastic model, broken into birth and death processes, was applied to analyze the current fluctuation and determine the physisorption energy. This method yields a highly sensitive, precise determination of the physisorption energy of molecules, and we include the physisorption energies for various molecules on a graphene nanostructure.

Graphene oxide papers modified by divalent ions-enhancing mechanical properties via chemical cross-linking

Significant enhancement in mechanical stiffness (10-200%) and fracture strength (approximately 50%) of graphene oxide paper, a novel paperlike material made from individual graphene oxide sheets, can be achieved upon modification with a small amount (less than 1 wt %) of Mg(2+) and Ca(2+). These results can be readily rationalized in terms of the chemical interactions between the functional groups of the graphene oxide sheets and the divalent metals ions. While oxygen functional groups on the basal planes of the sheets and the carboxylate groups on the edges can both bond to Mg(2+) and Ca(2+), the main contribution to mechanical enhancement of the paper comes from the latter.

Cyclotron resonance in bilayer graphene

We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B=18 T, we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow square root[B] for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However, in comparing data to theory, a single set of fitting parameters fails to describe the experimental results.

Chemically derived, ultrasmooth graphene nanoribbon semiconductors

We developed a chemical route to produce graphene nanoribbons (GNR) with width below 10 nanometers, as well as single ribbons with varying widths along their lengths or containing lattice-defined graphene junctions for potential molecular electronics. The GNRs were solution-phase-derived, stably suspended in solvents with noncovalent polymer functionalization, and exhibited ultrasmooth edges with possibly well-defined zigzag or armchair-edge structures. Electrical transport experiments showed that, unlike single-walled carbon nanotubes, all of the sub-10-nanometer GNRs produced were semiconductors and afforded graphene field effect transistors with on-off ratios of about 10(7) at room temperature.

High-energy limit of massless Dirac fermions in multilayer graphene using magneto-optical transmission spectroscopy

We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low-energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However, at higher energies (>500 meV) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is approximately 40 meV. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.

Vibrational analysis of single-layered graphene sheets

A molecular structural mechanics method has been implemented to investigate the vibrational behavior of single-layered graphene sheets. By adopting this approach, mode shapes and natural frequencies are obtained. Vibrational analysis is performed with different chirality and boundary conditions. Numerical results from the atomistic modeling are employed to develop predictive equations via a statistical nonlinear regression model. With the proposed equations, fundamental frequencies of single-layered graphene sheets with considered boundary conditions can be predicted within 3% difference with respect to the atomistic simulation.

Screening of coulomb impurities in graphene

We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, Z|e|/r, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter Zalpha, where alpha is the "fine-structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge Z(eff), determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, Z(eff)alpha<1/2, for any alpha, while impurities with Z=2, 3 and higher can become supercritical at certain values of alpha.

Flexural phonons in free-standing graphene

Rotation and reflection symmetries impose that out-of-plane (flexural) phonons of freestanding graphene membranes have a quadratic dispersion at long wavelength and can be excited by charge carriers in pairs only. As a result, we find that flexural phonons dominate the phonon contribution to the resistivity rho below a crossover temperature T(x) where we obtain an anomalous temperature dependence rho proportional, variantT(5/2)lnT. The logarithmic factor arises from renormalizations of the flexural-phonon dispersion due to coupling between bending and stretching degrees of freedom of the membrane.

Periodically rippled graphene: growth and spatially resolved electronic structure

We grow epitaxial graphene monolayers on Ru(0001) that cover uniformly the substrate over lateral distances larger than several microns. The weakly coupled graphene monolayer is periodically rippled and it shows charge inhomogeneities in the charge distribution. Real space measurements by scanning tunneling spectroscopy reveal the existence of electron pockets at the higher parts of the ripples, as predicted by a simple theoretical model. We also visualize the geometric and electronic structure of edges of graphene nanoislands.