Gapless Graphene Research Articles

Graphene-based non-Boolean logic circuits

Graphene revealed a number of unique properties beneficial for electronics. However, graphene does not have an energy band-gap, which presents a serious 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. Here we show that 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 gapless graphene. The negative differential resistance—observed under certain biasing schemes—is an intrinsic property of graphene, resulting from its symmetric band structure. Our atomistic modeling shows that the negative differential resistance appears not only in the drift-diffusion regime but also in the ballistic regime at the nanometer-scale—although the physics changes. The obtained results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.

Ballistic $I$– $V$ Characteristics of Short-Channel Graphene Field-Effect Transistors: Analysis and Optimization for Analog and RF Applications

With the recent upsurge in experimental efforts toward fabrication of short-channel graphene field-effect transistors (GFETs) for analog and high-frequency RF applications-where the advantages of distinctive intrinsic properties of gapless graphene are expected to be leveraged-a critical understanding of the factors affecting both output and transfer characteristics is necessary for device optimization. Analyzing the device characteristics through ballistic electronic transport simulations within the nonequilibrium Green's function formalism, we show that a doping in the drain underlap region can significantly improve the quasi-saturation behavior in the GFET output characteristics and, hence, the output resistance and intrinsic gain. From this understanding, we provide a unified and coherent explanation for seemingly disparate phenomena-quasi-saturation and the recently reported three-terminal negative differential resistance in GFETs. We also investigate the scaling behavior of cutoff frequency and comment on some of the observed scaling trends in recent experiments.

Inverse relationship between carrier mobility and bandgap in graphene

A frequently stated advantage of gapless graphene is its high carrier mobility. However, when a nonzero bandgap is opened, the mobility drops dramatically. The hardness to achieve high mobility and large on∕off ratio simultaneously limits the development of graphene electronics. To explore the underlying mechanism, we investigated the intrinsic mobility of armchair graphene nanoribbons (AGNRs) under phonon scattering by combining first-principles calculations and a tight-binding analysis. A linear dependence of the effective mass on bandgap was demonstrated to be responsible for the inverse mobility-gap relationship. The deformation-potential constant was found to be determined by the strain dependence of the Fermi energy and the bandgap, resulting in two mobility branches, and is essential for the high mobility of AGNRs. In addition, we showed that the transport polarity of AGNRs can be switched by applying a uniaxial strain.

SUBSTRATE MODULATED GRAPHENE QUANTUM DOTS

We propose a method to use gapped graphene as barriers to confine electrons in gapless graphene and form a good quantum dot, which can be realized on an oxygen-terminated SiO 2 substrate partly hydrogen-passivated. In particular, we use deposited ferromagnetic insulators as contacts which give rise to spin-dependent energy spectrum and transport properties. Furthermore, we upgrade this method to form two-dimensional quantum dot arrays, whose coupling strength between neighboring dots can be uniquely anisotropic. Compared to complexity of other approaches to form quantum dot in graphene, the setup suggested here is a promising candidate for practical applications.

CONDUCTIVITY OF GAPPED GRAPHENE WITHIN RANDOM PHASE APPROXIMATION

The gapped graphene is technologically more important as electronic devices made up of conventional semiconductors are based on the presence of a gap between the valence and conduction bands. In this paper, we report our analytical and numerical calculation of conductivity of gapped graphene on SiO 2 substrate and its variation with the governing parameters of carrier density, band gap, long range charge impurity scatterers, short range neutral defect scatterers, impurity distance from the graphene interface and potential strength of short range scattering centers. We find that the conductivity for unscreened potential decreases with increasing band gap but when screening is incorporated the trend is not only reversed but there is a sharp enhancement in its magnitude also. The sub linear behavior seen in conductivity in the case of gapless graphene at high carrier concentration due to enhanced scattering from the short range neutral defects is also observed for gapped graphene, and it is further observed that increasing the potential strength of the defect scatterers brings in the same behavior at relatively smaller carrier densities.

Anomalous growth of thermoelectric power in gapped graphene

There exist experiments indicating that at certain conditions, such as an appropriate substrate, a gap of the order of 10 meV can be opened at the Dirac points of a quasiparticle spectrum of graphene. We demonstrate that the opening of such a gap can result in the appearance of a fingerprint bump of the Seebeck signal when the chemical potential approaches the gap edge. The magnitude of the bump can be up to one order higher than the already large value of the thermopower occurring in graphene. Such a giant effect, accompanied by the nonmonotonous dependence on the chemical potential, is related to the emergence of a new channel of quasiparticle scattering from impurities with the relaxation time strongly dependent on the energy. We analyze the behavior of conductivity and thermopower in such a system, accounting for quasiparticle scattering from impurities with the model potential in a self-consistent scheme. Reproducing the existing results for the case of gapless graphene, we demonstrate a failure of the simple Mott formula in the case under consideration.

Landau level shift under the influence of short-range impurities in gapless graphene

We study theoretically the level shift of massless Dirac fermions in a graphene monolayer subjected to a quantizing perpendicular magnetic field under the influence of short-range impurities. A Green function method is used to obtain closed expressions for the Landau level shift for any sharply peaked impurity potential approaching a δ-shell potential.

Electronic properties of bearded graphene nanoribbons

We investigate the electronic properties of graphene nanoribbons with attachment of bearded bonds as a model of edge modification. The main effect of the addition of the beards is the appearance of additional energy subbands. The originally gapless armchair graphene nanoribbons become semiconducting. On the other hand, the originally semiconducting armchair graphene nanoribbons may or may not change to gapless systems depending on the width. With the inclusion of a transverse electric field, the band structures of bearded graphene nanoribbons are further altered. An electric field creates additional band-edge states, and changes the subband curvatures and spacings. Furthermore, the energy band symmetry about the chemical potential is lifted by the field. With varying width, the bandgap demonstrates a declining zigzag behavior, and touches the zero value regularly. Modifications in the electronic structure are reflected in the density of states. The numbers and energies of the density of state divergent peaks are found to be strongly dependent on the geometry and the electric field strength. The beard also causes electron transfer among different atoms, and alters the probability distributions. In addition, the electron transfers are modified by the electric field. Finally, the field introduces more zero values in the probability distributions, and removes their left–right symmetry.

Energy loss spectroscopy of epitaxial versus free-standing multilayer graphene

We present a formalism and numerical results for the energy loss of a charged particle scattered at an arbitrary angle from epitaxially grown multilayer graphene (MLG). It is compared with that of free-standing graphene layers. Specifically, we investigated the effect of the substrate induced energy gap on one of the layers. The gap yields collective plasma oscillations whose characteristics are qualitatively and quantitatively different from those produced by Dirac fermions in gapless graphene. The range of wave numbers for undamped self-sustaining plasmons is increased as the gap is increased, thereby substantially increasing and red-shifting the MLG stopping power for some range of charged particle velocity. We also applied our formalism to interpret several distinct features of experimentally obtained electron energy loss spectroscopy (EELS) data.

Valley-dependent tunneling in a monolayer gapped graphene without strain

Transmission of massive Dirac fermions in a monolayer-gapped-graphene PF/N/PF pseudo spin valve is investigated where PF is a pseudo ferromagnet caused by gap opening in graphene and N is a normal graphene sheet without energy gap. We find that, significantly, in asymmetric junction although the system has no local strain field, the valley-dependent transmission in the angular space is observed. Such transmission acting like that of electron tunneling under strain field is not observed in case of gapless graphene, saying that it is related to the influence of energy gap-like relativistic mass in graphene. We also find that, similar to fermionic field in topological insulators, energy gap between valence and conduction bands in graphene could be considered as both mass and vector potential. Our work reveals a new way to control valley currents in monolayer graphene using a gap opening, instead of using strain. It is also important for fundamental study of physics of graphene and applications of valleytronic devices.

Size quantization in planar graphene-based heterostructures: Pseudospin splitting, interface states, and excitons

A planar quantum-well device made of a gapless graphene nanoribbon with edges in contact with gapped graphene sheets is examined. The size-quantization spectrum of charge carriers in an asymmetric quantum well is shown to exhibit a pseudospin splitting. Interface states of a new type arise from the crossing of dispersion curves of gapless and gapped graphene materials. The exciton spectrum is calculated for a planar graphene quantum well. The effect of an external electric field on the exciton spectrum is analyzed.

Dirac donor states controlled by magnetic field in gapless and gapped graphene

In this paper, the exact solutions of Dirac electronic states of graphene in Coulomb and magnetic fields are acquired. The Coulomb field not only causes the splitting of Landau levels in gapless graphene but also leads to the variation of the energy level ordering in gapped graphene. The dependence of the binding energies on the gap and the magnetic field is discussed. Furthermore, the valley degree of freedom and the valley splitting spacing can be controlled by the Coulomb and magnetic fields in gapped graphene. The intervalley mixing of graphene is estimated and calculated in the direct sum spaces of the two valleys. The results obtained help us to understand the behaviors of the planar Dirac electron in electromagnetic fields and can be applied to the controlling of the electron's behaviors in graphene.

Graphene nanomesh-based devices exhibiting a strong negative differential conductance effect

Using atomistic quantum simulation based on a tight binding model, we have investigated the transport characteristics of graphene nanomesh-based devices and evaluated the possibilities of observing negative differential conductance. It is shown that by taking advantage of bandgap opening in the graphene nanomesh lattice, a strong negative differential conductance effect can be achieved at room temperature in pn junctions and n-doped structures. Remarkably, the effect is improved very significantly (with a peak-to-valley current ratio of a few hundred) and appears to be weakly sensitive to the transition length in graphene nanomesh pn hetero-junctions when inserting a pristine (gapless) graphene section in the transition region between n and p zones. The study therefore suggests new design strategies for graphene electronic devices which may offer strong advantages in terms of performance and processing over the devices studied previously.

Spectroscopic characterization of gapped graphene in the presence of circularly polarized light

We present a description of the energy loss of a charged particle moving parallel to a graphene layer and graphene double layers. Specifically, we compare the stopping power of the plasma oscillations for these two configurations in the absence as well as the presence of circularly polarized light whose frequency and intensity can be varied to yield an energy gap of several hundred meV between the valence and conduction bands. The dressed states of the Dirac electrons by the photons yield collective plasma excitations whose characteristics are qualitatively and quantitatively different from those produced by Dirac fermions in gapless graphene, due in part to the finite effective mass of the dressed electrons. For example, the range of wave numbers for undamped self-sustaining plasmons is increased as the gap is increased, thereby increasing the stopping power of graphene for some range of charged particle velocity when graphene is radiated by circularly polarized light.

Radio-Frequency Transistors Using Chemical-Vapor-Deposited Monolayer Graphene: Performance, Doping, and Transport Effects

Large-area graphene is synthesized by Cu-catalyzed chemical vapor deposition (CVD), transistors are constructed, and the dc/RF performance is examined. Top-gate transistors, i.e., with a gate length of 3 μm and V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ds</sub> = 5 V, have a peak dc transconductance in excess of 20 mS/mm and a drive current of 0.5 A/mm. RF measurements achieve gigahertz extrinsic current-gain cutoff frequency with low back biasing. Back-gated devices are used to examine doping and transport effects that impact the performance. Good agreement between measurements and a drift-diffusion model is obtained for gapless graphene with a net p-type doping and asymmetric electron/hole mobility. The mean free path for scattering is extracted and reveals that the transport suffers from large levels of Coulomb scattering and short-range scattering. The results are of importance for understanding the performance potential of large-area CVD graphene in future RF devices.

Single-side-hydrogenated graphene: Density functional theory predictions

Hydrogenation has proven to be an effective tool to open the band gap of graphene. In the present density functional study, we demonstrate that single-side-hydrogenated graphene is a semiconductor with an indirect band gap of 1.35 eV, which is in between the gapless graphene and wide band-gap graphane and surprisingly close to silicon. We show that its electronic structure and lattice characteristics are substantially different from those of graphene, graphone, or graphane. The lattice parameter and C-C bond length are found to be lengthened by $15%$ of those of graphene. Our binding-energy analysis confirms that such a single-sided hydrogenation leads to energetically stable material, making it a promising candidate as an organic semiconductor.

Josephson Current in a Gapped Graphene Superconductor/Barrier/Superconductor Junction: Case of Massive Electrons

The Josephson effect in a gapped graphene-based superconductor/barrier/superconductor junction is studied. The superconductivity in gapped graphene may be achieved by depositing conventional superconductor on the top of the gapped graphene such as graphene grown on SiC substrate. In gapped graphene system, the carriers exhibit massive Dirac fermions. We focus on the effect of pseudo-Dirac-like mass on the supercurrent. In contrast to that in the gapless graphene superconductor/barrier/superconductor junction, we find that the supercurrent exhibits dependency of the Fermi energy. Also, the massive supercurrent anomalously oscillates as a function of the gate potential. This novel behavior is due to the effect of electrons acquiring mass in gapped graphene.

Effect of topology on the critical charge in graphene

We show that the critical charge for the Dirac excitations in gapless graphene depends on the spatial topology of the sample. In particular, for graphene cones, the effective value of the critical charge can tend towards zero for a suitable angle of the conical sample. We discuss the nature of the scattering phase shifts, quasi-bound state energies and local density of states for a gapless graphene cone and determine the dependence of these physical quantities on the sample topology.

Subgap optical conductivity in semihydrogenated graphene

We report that for graphene with a finite band gap (such as semihydrogenated graphene or graphene with spin-orbit coupling), there exists a strong nonlinear optical response for energies lower than the band gap where the linear response is forbidden. At low temperatures, the nonlinear current in graphene with a gap is much stronger than that in gapless graphene. Our result suggests that semihydrogenated graphene can have a unique potential as a two-color nonlinear material in the terahertz frequency region. The relative intensity of the two colors can be tuned with the electric field.

Magneto-transport properties of gapped graphene

Based on the Kubo formula, we have studied the electron transport properties of a gappedgraphene in the presence of a strong magnetic field. By solving the Dirac equation, we findthat the Landau level spectra in two valleys differ from each other in that then = 0 level inthe K valley is located at top of the valence band, whereas it is at the bottom of the conduction band in theK′ valley. Thus, in an individual valley, the symmetry between conduction and valencebands is broken by the presence of a magnetic field. By using the self-consistentBorn approximation to treat the long range potential scattering, we formulate thediagonal and the Hall conductivities in terms of the Green function. To performthe numerical calculation, we find that a large bandgap can suppress thequantum Hall effect, owing to the enhancement of the bandgap squeezing thespacing between the low-lying Landau levels. On the other hand, if the bandgap isnot very large, the odd integer quantum Hall effect experimentally, observed inthe gapless graphene, remains in the gapped one. However, such a result doesnot indicate the half integer quantum Hall effect in an individual valley of thegapped graphene. This is because the heights of the Hall plateaux in either valleycan be continuously tuned by the variation of the bandgap. More interestingly,we find that the height of the diagonal conductivity peak corresponding to then = 0 Landau level is independent of the bandgap if the scattering is not very strong. In the weakscattering limit, we demonstrate analytically that such a peak takes a universal valuee2/(hπ), regardless of the bandgap.