Search

We propose to control of an electron-hole superfluid in semiconductor coupled quantum wells and double layers of two-dimensional (2D) material by an external periodic field. This can either be created by the gates periodically located and attached to the quantum wells or double layers of 2D material or by the Moir\'e pattern of two twisted layers. The dependence of the electron-hole pairing order parameter on the temperature, the charge carrier density, and the gate parameters is obtained by minimization of the mean-field free energy. The second order phase transition between superfluid and electron-hole plasma, controlled by the external periodic gate field, is analyzed for different parameters., Comment: 10 pages, 4 figures

A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong influence on the electromagnetic field and its polarization inside the sample. The creation of edge states through a randomly fluctuating sign of the Dirac mass defeats Anderson localization and allows the electromagnetic field to distribute over the entire sample. The width of the distribution increases with an increasing gap due to increasing sharpness of the edge states. These results are compared with those of a random one-band Helmholtz equation. In contrast to the Dirac model, the one-band model displays a clear signature of Anderson localization., Comment: 12 pages, 12 figures

Edge states are studied for the two-dimensional Dirac equation in a circular geometry. The properties of the two-component electromagnetic field are discussed in terms of the three-component polarization field, which can form a vortex structure near the Dirac node with a vorticity changing with the sign of the Dirac mass. The Berry curvature of the polarization field is related to the Berry curvature of the Dirac spinor state. This quantity is sensitive to a change of boundary conditions. In particular, it vanishes for a geometry with a single boundary but not for a geometry with two boundaries. This effect is robust against the creation of a step-like edge inside the sample., Comment: 8 pages, 5 figures

The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. Here we consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band structure on the optical conductivity and on diffusion due to quantum fluctuations. In contrast to the behavior at an isotropic node we find super- and subdiffusion for the anisotropic node. The spectral saddle points create van Hove singularities in the optical conductivity, which could be used to characterize the spectral properties experimentally., Comment: 9 pages, 6 figures. Slightly extended version, e.g. Eq.(12) included

We calculate the transport properties of three-dimensional Weyl fermions in a disordered environment. The resulting conductivity depends only on the Fermi energy and the scattering rate. First we study the conductivity at the spectral node for a fixed scattering rate and obtain a continuous transition from an insulator at weak disorder to a metal at stronger disorder. In the self-consistent Born approximation the scattering rate depends on the Fermi energy. Then it is crucial that the limits of the conductivity for a vanishing Fermi energy and a vanishing scattering rate do not commute. As a result, there is also metallic behavior in the phase with vanishing scattering rate and only a quantum critical point remains as an insulating state., Comment: 9 pages, 5 figures

A study of the formation of excitons as a problem of two Dirac particles in a gapped graphene layer and in two gapped graphene layers separated by a dielectric is presented. In the low energy limit the separation of the center-of-mass and relative motions is obtained. Analytical solutions for the wave function and energy dispersion for both cases when electron and hole interact via a Coulomb potential are found. It is shown that the energy spectrum and the effective exciton mass are functions of the energy gaps as well as interlayer separation in case of two layer gapped graphene., Comment: 12 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1110.6744

The optical conductivity for the surface excitations for a Topological Insulator as a function of the chemical potential and disorder is considered. Due to the time reversal symmetry the chiral metallic surface states are protected against disorder. This allow to use the averaged single particle Green's function to compute the optical conductivity. We compute the conductivity in the limit of a finite disorder. We find that the conductivity as a function of the chemical potential $\mu $ and frequency $\Omega$ is given by the universal value $\sigma(\Omega>2\mu)= \frac{e^2 \pi}{8h}$. For frequencies $\Omega< \mu$ and elastic mean free path $l_{el}=v\tau$ which obey $k_{F}l>1$ we obtain the conductivity is given by $\sigma(\Omega<2|\mu|)=\frac{e^2}{2h}\frac{k_{F}l_{el}}{(\Omega \tau)^2+1}$. In the limit of zero disorder we find $\sigma(\mu\neq0,\Omega, k_{F}l\rightarrow \infty)=\frac{e^2 \pi}{2h}|\mu|\delta(\Omega)$.

In this paper we investigate the influence of the next-nearest-neighbor coupling of tight-binding model of graphene on the spectrum of plasmon excitations. The nearest-neighbor tight-binding model was previously used to calculate plasmon spectrum in the next paper [1]. We expand the previous results of the paper by the next-nearest-neighbor tight-binding model. Both methods are based on the numerical calculation of the dielectric function of graphene and loss function. Here we compare plasmon spectrum of the next-nearest and nearest-neighbor tight-binding models and find differences between plasmon dispersion of two models., Comment: LaTeX, 4 pages, 4 Figs

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice., Comment: 189 pages. submitted in Advances in Physics

We study the DC transport of finite graphene samples with random gap. Using Dirac fermions to describe the low-energy physics near the Dirac point, we employ a generalized Drude form for the conductivity. The latter is constant for a vanishing average gap but always decreases with increasing sample size for a nonzero average gap. The asymptotic conductivity of the infinite sample is either nonzero if the average gap is smaller than a critical value or zero otherwise. Our results are in agreement with recent numerical calculations of Bardarson et al.., Comment: 4 pages, improved figures, 2 figures added

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence., Comment: 10 pages, 12 figures, additional references added

We have performed a theoretical study of electronic transport in single and bilayer graphene based on the standard linear-response (Kubo) formalism and continuum-model descriptions of the graphene band structure. We are focusing especially on the interband contribution to the optical conductivity. Analytical results are obtained for a variety of situations, which allow clear identification of features in the conductivity that are associated with relevant electronic energy scales. Our work extends previous numerical studies and elucidates ways to infer electronic properties of graphene samples from optical-conductivity measurements., Comment: 4 pages, 2 figures, contribution to EP2DS-18, to appear in Physica E

The effect of a randomly fluctuating gap, created by a random staggered potential, is studied in a monolayer and a bilayer of graphene. The density of states, the one-particle scattering rate and transport properties (diffusion coefficient and conductivity) are calculated at the neutrality point. All these quantities vanish at a critical value of the average staggered potential, signaling a continuous transition to an insulating behavior. The calculations are based on the self-consistent Born approximation for the one-particle scattering rate and a massless mode of the two-particle Green's function which is created by spontaneous symmetry breaking. Transport quantities are directly linked to the one-particle scattering rate. Moreover, the effect of disorder is very weak in the case of a monolayer but much stronger in bilayer graphene., Comment: 5 pages, 1 figure

We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters., Comment: 5 pages, 4 figures

The appearence of long-range correlations near the Dirac point of a Dirac-like spinor model with random vector potential is studied. These correlations originate from a spontaneously broken symmetry and their corresponding Goldstone modes. Using a strong-disorder expansion, correlation functions and matrix elements are analyzed and compared with results from a weak-disorder expansion. The local density of states correlation and the overlap between states above and below the Dirac point are characterized by a long-range behavior. The correlation range decreases with the distance from the Dirac point. Transport is diffusive and the diffusion coefficient is proportional to the one-particle scattering time for any strength of disorder. A consequence of the special properties of particle-hole scattering is a constant microwave conductivity for weak as well as for strong disorder, describing a deviation from conventional Drude-like transport. Some properties of the model can be linked to a kind of Kondo scale, which is generated by disorder. Finally, the properties of the wave functions at the Dirac point are characterized by their participation ratios, indicating a critical state at the Dirac point., Comment: 17 pages, 3 figures

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, electromagnetic response of graphene is predicted to be strongly non-linear. We develop a quasi-classical kinetic theory of the non-linear electromagnetic response of graphene, taking into account the self-consistent-field effects. Response of the system to both harmonic and pulse excitation is considered. The frequency multiplication effect, resulting from the non-linearity of the electromagnetic response, is studied under realistic experimental conditions. The frequency up-conversion efficiency is analysed as a function of the applied electric field and parameters of the samples. Possible applications of graphene in terahertz electronics are discussed., Comment: 14 pages, 7 figures, invited paper written for a special issue of JPCM "Terahertz emitters"

The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we conclude, that the linear density of states of pure graphene changes to a non-universal power-law, whose exponent depends on the strength of disorder like 1-4g/sqrt{3}t^2\pi, with g the variance of the Gaussian disorder, t the hopping integral. This can result in a significant suppression of the exponent of the density of states in the weak-disorder limit. We argue, that even a non-linear density of states can result in a conductivity being proportional to the number of charge carriers, in accordance with experimental findings., Comment: 7 pages, 5 figures

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. Surprisingly, the magnetic field drops out of the transport quantities in leading order of this expansion. This signals a strong suppression of magnetotransport effects for sufficiently strong disorder. This result is consistent with recent experimental observations by Morozov {\it et al.}, Comment: 5 pages, 2 figures

A new, weakly damped, {\em transverse} electromagnetic mode is predicted in graphene. The mode frequency $\omega$ lies in the window $1.667<\hbar\omega/\mu<2$, where $\mu$ is the chemical potential, and can be tuned from radiowaves to the infrared by changing the density of charge carriers through a gate voltage., Comment: 5 pages, 4 figures

A two-dimensional gas of non-interacting quasiparticles in a nearly periodic potential is considered at zero temperature. The potential is a superposition of a periodic potential, induced by the charge density wave of a Wigner crystal, and a weak random potential due to disorder. There is a metal-insulator transition that is controlled by the strength of the periodic potential. The transition is continuous in the presence of randomness. We evaluate the density of states, which is non-zero at the Fermi energy in the metallic phase, and the dc conductivity. The latter changes with decreasing modulation of the periodic potential from 0 to $\sigma\approx2e^2/h$., Comment: 4 pages, 3 figures

A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb coupling., Comment: 6 pages incl 3 figures

The dynamical transport properties near the integer quantum Hall transition are investigated at zero temperature by means of the Dirac fermion approach. These properties have been studied experimentally at low frequency omega and low temperature near the nu=1 filling factor Hall transition, with the observation of an anusual broadening and an overall increase of the longitudinal conductivity Re sigma_{xx} as a function of omega. We find in our approach that, unlike for normal metals, the longitudinal conductivity increases as the frequency increases, whilst the width Delta B (or Delta nu) of the conductivity peak near the Hall transition increases. These findings are in reasonable quantitative agreement with recent experiments by Engel et al. as well as with recent numerical work by Avishai and Luck., Comment: 8 pages, 3 figures, to appear in Phys. Rev. B

A two-dimensional gas of non-interacting quasiparticles in a nearly periodic potential and a perpendicular magnetic field is studied. The potential is a superposition of a periodic potential, induced e.g. by a charge density wave or a vortex lattice of a type--II superconductor, and a weak random potential due to impurities. Approximating this model by Dirac fermions with random mass, random energy, and random vector potential, we evaluate the density of states and the Hall conductivity using a self-consistent approximation. We obtain a singular average density of states $\rho(E)\approx\rho_0 +|E|^\alpha$, where $\alpha$ decreases with the strength of randomness. The Hall conductivity has a plateau which is destroyed for strong tunneling through the saddle points of the nearly periodic potential., Comment: 10 pages, 4 figures, J. Phys. C (in press)

The mechanism of delocalization of two-dimensional Dirac fermions with random mass is investigated, using a superfield representation. Although localization effects are very strong, one fermion component can delocalize due to the spontaneous breaking of a special supersymmetry of the model. The delocalized fermion has a non-singular density of states and is decribed by a diffusion propagator. Supersymmetry is restored if the mean of the random mass is sufficiently large. This is accompanied by a critical boson component., Comment: 4 pages

We present a calculation for the second moment of the local density of states in a model of a two-dimensional quantum dot array near the quantum Hall transition. The quantum dot array model is a realistic adaptation of the lattice model for the quantum Hall transition in the two-dimensional electron gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and Grinstein. We make use of a Dirac fermion representation for the Green functions in the presence of fluctuations for the quantum dot energy levels. A saddle-point approximation yields non-perturbative results for the first and second moments of the local density of states, showing interesting fluctuation behaviour near the quantum Hall transition. To our knowledge we discuss here one of the first analytic characterizations of chaotic behaviour for a two-dimensional mesoscopic structure. The connection with possible experimental investigations of the local density of states in the quantum dot array structures (by means of NMR Knight-shift or single-electron-tunneling techniques) and our work is also established., Comment: 11 LaTeX pages, 1 postscript figure, to appear in Phys.Rev.B

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance $g$ is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity $\sigma_{xx}$ was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that $\sigma_{xx}$ is reduced by a factor $(1+g/2\pi)^{-1}$, at least for small $g$. This provides some theoretical evidence for the non-universality of $\sigma_{xx}$, as observed in a number of experiments., Comment: 2 double-column LaTeX pages, no figures, to appear in Z.Phys.B

A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective fields is constructed and studied within saddle point approximation and fluctuations. The model is characterized by a broken supersymmetry indicating that only the fermion collective field becomes delocalized whereas the boson field is exponentially localized. Power counting for the fluctuation terms suggests that the interactions between delocalized fluctuations are irrelevant. Several quasi--scaling regimes, separated by large cross--over lengths, are found with effective exponents $\nu$ for the localization length $\xi_l$. In the asymptotic regime there is $\nu=1/2$ in agreement with an earlier calculation of Affleck and one by Ludwig et al. for finite density of states. The effective exponent, relevant for physical system, is $\nu=1$ where the coefficient of $\xi_l$ is growing with randomness. This is in agreement with recent high precision measurements on Si MOSFET and AlGaAs/GaAs samples., Comment: 25 pages, RevTeX, 2 figures, to appear in Phys.Rev. B