Related papers: Dirac-Schrodinger transformations in contacted gra…
A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schrodinger equation, electronic…
We study the interaction of electrons in graphene with the quantized electromagnetic field in the presence of an applied uniform electric field using the Dirac model of graphene. Electronic states are represented by exact solutions of the…
The perfect transmission of charge carriers through potential barriers in graphene (Klein tunneling) is a direct consequence of the Dirac equation that governs the low-energy carrier dynamics. As a result, localized states do not exist in…
Exact stationary solutions of the electron-photon Dirac equation are obtained to describe the strong interaction between massless Dirac fermions in graphene and circularly polarized photons. It follows from them that this interaction forms…
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…
The electrons in graphene for energies close to the Dirac point have been found to form strongly interacting fluid. Taking this fact into account we have extended previous work on the transport properties of graphene by taking into account…
Conductance of zigzag interfaces between graphene sheet and normal metal is investigated in the tight-binding approximation. Boundary conditions, valid for a variety of scattering problems, are constructed and applied to the normal metal --…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
Dirac energy-dispersions are responsible of the extraordinary transport properties of graphene. This motivated the quest for engineering such energy dispersions also in photonics, where they have been predicted to lead to many exciting…
The paper reports a theoretical study of scattering of electrons by edges in graphene and its effect on Raman scattering. First, effective models are discussed for translationally invariant and rough edges. Second, they are used in a…
We study theoretically the interaction of twisted light with graphene. The light-matter interaction matrix elements between the tight-binding states of electrons in graphene are determined near the Dirac points. We examine the dynamics of…
A generalized Dirac equation is derived in order to describe charge carriers moving in corrugated graphene, which is the case for temperatures above 10{\deg}K due to the presence of flexural phonons. Such interaction is taken into account…
A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In…
In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to…
Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from…
The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy…
The Dirac equation in curved space is used to study the optical transmittance of deformed graphene along a given direction. Our theoretical analysis of the available experimental data for the light transmittance suggests that the periodic…
This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric…
The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on…
A new transport regime of photon in two-dimensional photonic crystal near the Dirac point has been demonstrated by exact numerical simulation. In this regime, the conductance of photon is inversely proportional to the thickness of sample,…