Among the many interesting features displayed by graphene, one of the most attractive is the simplicity with which its electronic structure can be described. The study of its physical properties is significantly simplified by the linear dispersion relation of electrons in a narrow range around the Fermi level. Unfortunately, the mathematical simplicity of graphene electrons is only limited to this narrow energy region and is useless when dealing with problems that involve energies outside the linear dispersion part of the spectrum. In this letter we remedy this limitation by deriving a set of closed-form analytical expressions for the real-space single-electron Green function of graphene which are valid across an enormous fraction of the energy spectrum. By extending to a wider energy range the simplicity with which graphene electrons are described, it is now possible to derive more mathematically transparent and insightful expressions for a number of physical properties that involve higher energy scales. The power of this new formalism is illustrated in the case of the magnetic (RKKY) interaction in graphene.
Dispersion of "Dispersionless Zero Mode": Comments on L. Brey and H.A. Fertig paper Electronic States of Graphene Nanoribbons Studied With The Dirac Equation
We study the effects of $δ$-function periodic kicks on the Floquet energy-momentum dispersion in graphene. We find that a rich variety of dispersions can appear depending on the parameters of the kicking: at certain points in the Brillouin zone, the dispersion can become linear but anisotropic, linear in one direction and quadratic in the perpendicular direction, gapped with a quadratic dispersion, or completely flat (called dynamical localization). We show all these results analytically and demonstrate them numerically through the dynamics of wave packets propagating in graphene. We propose e…
The acoustoelectric effect $AE$ in Graphene with degenerate energy dispersion is theoretically studied for hypersound in the regime $ql >> 1$. At low temperatures ($k_βT <<1$), the non-linear dependence of Acoustoelectric current $j/j_0$ on the frequency $ω_q$ and temperature $T$ are numerically analysed. The obtained graph for $j/j_0$ against $ω_q$ qualitatively agreed with an experimentally obtained results. For $j/j_0$ versus $T$, the dependence of Acoustoelectric current in Graphene was found to manifest at low temperatures.
The dispersion relation for magnetoplasmons in a planar superlattice with periodically alternating regions of gapless and gapped modications of graphene has been derived within the frame of the random-phase approximation. The contribution of virtual transitions between the lower electron miniband and the upper hole miniband to the polarization operator has been taken into account in addition to the contribution of virtual intra-miniband transitions.
Plasma oscillations in doped graphene bilayer at zero temperature has been investigated. Bias voltage effect on the dispersion curve for plasmon in bigraphene has been studied in random phase approximation. The possibility of controlling of curvature of dispersion curve for plasmon by changing of bias voltage has been shown. The dependence of this curvature on the bias voltage has been predicted to have the nonmonotonous character. Namely the existence of breaking point for such dependence has been found out. The bias voltage corresponding to the breaking point is shown to increase with free c…
Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition
Hypersound amplification/absorption of acoustic phonons in Graphene with degenerate energy dispersion $\varepsilon(p)$ near the Fermi level was theoretically studied. For $k_βT << 1$ and $ql >> 1$, the dependence of the absorption coefficient $Γ/Γ_0$ on ${V_D\over V_s}$ was studied where the results satisfied the Cerenkov effect. That is when ${V_D\over V_s} > 1$, an amplification was obtained but for ${V_D\over V_s} < 1$, an absorption was obtained which could lead to Acoustoelectric Effect (AE) in Graphene. A linear dependence of the $Γ/Γ_0$ on $ω_q$ was observed where the result obtianed qu…
Previous studies of electron-phonon interaction in impure graphene have found that static disorder can give rise to an enhancement of electronic cooling. We investigate the effect of dynamic disorder and observe over an order of magnitude suppression of electronic cooling compared with clean graphene. The effect is stronger in graphene with more vacancies, confirming its vacancy-induced nature. The dependence of the coupling constant on the phonon temperature implies its link to the dynamics of disorder. Our study highlights the effect of disorder on electron-phonon interaction in graphene. In…
We report the direct observation of polarization resolved electronic Raman scattering in a gated monolayer graphene device. The evolution of the electronic Raman scattering spectra with gate voltage and its polarization dependence are in full agreement with theoretical expectations for non-resonant Raman processes involving interband electron-hole excitations across the Dirac cone. We further show that the spectral dependence of the electronic Raman scattering signal can be simply described by the dynamical polarizability of graphene in the long wavelength limit. The possibility to directly ob…
Magnetotransport measurements on Hall bar devices fabricated on purely monolayer epitaxial graphene on Silicon Carbide (SiC/G) show a very tight spread in carrier concentration and mobility across wafer- size dimensions. In contrast, SiC/G devices containing bilayer graphene domains display variations in their electronic properties linked to the amount of bilayer content.
Non-covalent functionalization via physisorption of organic molecules provides a scalable approach for modifying the electronic structure of graphene while preserving its excellent carrier mobilities. Here we investigated the physisorption of long-chain acenes, namely, hexacene and its fluorinated derivative perfluorohexacene, on bilayer graphene for tunable graphene devices using first principles methods. We find that the adsorption of these molecules leads to the formation of localized states in the electronic structure of graphene close to its Fermi level, which could be readily tuned by an…
The experimental control over the twist angle in twisted bilayer graphene has not been reported and its realistic structure is most likely incommensurate. In this paper, we develop a tight-binding virtual crystal approximation theory to study the electronic properties in incommensurate twisted bilayer graphene. The theory yields the electronic band structure and the local density of states for any incommensurate twist angle θ between the graphene sheets. Angle dependent Van Hove singularities are observed in the numerically calculated local density of states. In accord with observations in sca…
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken, by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a novel bilayer graphene heterostructure, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band structure engineering can be performed to obtain linearly dispersi…
We demonstrate that single layer graphene exhibits the electronic structure of a bilayer when it is connected to two gated bilayers. The energy gap characteristic for gated bilayer is induced in the single layer and it persists for distances separating the bilayers up to 20 nm. Most importantly, we report on the appearance of topologically protected gapless state localized in a single graphene layer when the distant bilayers differ in the stacking order. The one-dimensional current in the topological state flows in a single layer graphene, and this finding suggests a new exploitation of graphe…
Atomically precise armchair graphene nanoribbons of width $N=7$ (7-AGNRs) are investigated by scanning tunneling spectroscopy (STS) on Au(111). The analysis of energy-dependent standing wave patterns of finite length ribbons allows, by Fourier transformation, the direct extraction of the dispersion relation of frontier electronic states. Aided by density functional theory calculations, we assign the states to the valence band, the conduction band and the next empty band of 7-AGNRs, determine effective masses of $0.42\pm 0.08\,m_e$, $0.40\pm 0.18\,m_e$ and $0.20\pm 0.03\,m_e$, respectively, and…
In this paper we introduce a new structure similar to the graphane which we call it penta graphane. This structure is obtained by adding hydrogen to penta graphene bond. We study the electronic and phononic structure of penta graphane. We firstly use with the generalized gradient approximation to compute the band structure.
We theoretically investigate the electronic transport properties of curved graphene waveguides by employing non-equilibrium Green's function techniques. We systematically study the dependence of the confined waveguide modes on the potential difference, the width of waveguide and side barrier. Through two-terminal electronic transport calculations, we show that the conductance of confined waveguide modes is rather robust against the bending degree of waveguide, in consistent with the band insensitivity to the side barrier. This finding of the perfectly conducting channels strongly suggests the …
We combine {\em ab initio} density functional theory (DFT) structural studies with DFT-based nonequilibrium Green function calculations to investigate how the presence of non-hexagonal rings affects electronic transport in graphitic structures. We find that infinite monolayers, finite-width nanoribbons and nanotubes formed of 5-8 haeckelite with only 5- and 8-membered rings are generally more conductive than their graphene-based counterparts. Presence of haeckelite defect lines in the perfect graphitic structure, a model of grain boundaries in CVD-grown graphene, increases the electronic condu…
We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near the Fermi level, but also that of twisted bilayer graphene including the value of the magic angle, at which bands at $E_F$ flatten without overlap and two gaps open, one above and one below $E_F$. The Hamiltonian is sufficiently transparent and flexible to be adopted to other twisted layered systems.
Allotropes of carbon, including one-dimensional carbon nanotubes and two-dimensional graphene sheets, continue to draw attention as promising platforms for probing the physics of electrons in lower dimensions. Recent research has shown that the electronic properties of graphene multilayers are exquisitely sensitive to the relative orientation between sheets, and in the bilayer case exhibit strong electronic correlations when close to a magic twist angle. Here, we investigate the electronic properties of a carbon nanotube deposited on a graphene sheet by deriving a low-energy theory that accoun…
Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic pre-turbulence in graphene samples. In particular, pre-turbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.
Excitation of surface plasmon waves in extrinsic graphene is studied using a full-wave electromagnetic field solver as analysis engine. Particular emphasis is placed on the role played by spatial dispersion due to the finite size of the two-dimensional material at the micro-scale. A simple instructive set up is considered where the near field of a wire antenna is held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of the simulation is the graphene conductivity tensor at terahertz frequencies, being modeled by the Boltzmann transport equation for the valence and co…
