Related papers: Dirac fermions in a power-law-correlated random ve…
We study the behavior of two-dimensional Dirac fermions in the presence of a static long-range-correlated random vector potential. By applying an exact path integral representation for the propagator of a spinor particle we obtain…
We develop a microscopic theory of the weak localization of two-dimensional massless Dirac fermions which is valid in the whole range of classically weak magnetic fields. The theory is applied to calculate magnetoresistance caused by the…
We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of…
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in…
System of Dirac fermions with random-varying mass is studied in detail. We reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random telegraphic mass…
We study the effect of the curved ripples observed in the free standing graphene samples on the electronic structure of the system. We model the ripples as smooth curved bumps and compute the Green's function of the Dirac fermions in the…
This review aims at a theoretical discussion of Dirac points in two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in…
We consider 2D Dirac fermions in the presence of three types of disorder: random scalar potential, random gauge potential and random mass with long-range correlations decaying as a power law. Using various methods such as the…
The electromagnetic response of graphene, expressed by the dielectric function, and the spectrum of collective excitations are studied as a function of wave vector and frequency. Our calculation is based on the full band structure,…
Generalizing the notion of composite fermions to the "pseudo-relativistic" Quantum Hall phenomena in graphene, we discuss a possible emergence of compressible states at the filling factors -3/2, -1/2, 1/2, 3/2. This analysis is further…
We study the influence of a localized Gaussian deformation on massless Dirac fermions confined to a two-dimensional curved surface. Both in-plane and out-of-plane displacements are considered within the framework of elasticity theory. These…
An analysis of the electron localization properties in doped graphene is performed by doing a numerical multifractal analysis. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions…
We report the formation of bound states in the continuum for Dirac-like fermions in structures composed by a trilayer graphene flake connected to nanoribbon leads. The existence of this kind of localized states can be proved by combining…
In this and subsequent papers, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the…
Graphene is a unique two-dimensional material with rich new physics and great promise for applications in electronic devices. Physical phenomena such as the half-integer quantum Hall effect and high carrier mobility are critically dependent…
A system in a quantum superposition of distinct states usually exhibits many peculiar behaviors. Here we show that putting quasiparticles of graphene into superpositions of states in the two valleys can complete change the properties of the…
Two-dimensional carbon, or graphene, is a semi-metal that presents unusual low-energy electronic excitations described in terms of Dirac fermions. We analyze in a self-consistent way the effects of localized (impurities or vacancies) and…
We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accomodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment…
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…
We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to…