相关论文: Energy levels of triangular and hexagonal graphene…

We investigate nonlinear Dirac equations on a periodic quantum graph $G$ and develop a variational approach to the existence and multiplicity of bound states. After introducing the Dirac operator on $G$ with a $\mathbb Z^{d}$-periodic…

We study the energy levels of carriers confined in a magnetic quantum dot of graphene surrounded by a infinite graphene sheet in the presence of energy gap. The eigenspinors are derived for the valleys $K$ and $K'$, while the associated…

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen…

The electronic properties of graphene zig-zag nanoribbons with electrostatic potentials along the edges are investigated. Using the Dirac-fermion approach, we calculate the energy spectrum of an infinitely long nanoribbon of finite width…

In this article, we study topological and noninertial effects on the motion of the two-dimensional Dirac oscillator in the presence of a uniform magnetic field and the Aharonov-Bohm potential. We obtain the Dirac equation that describes the…

We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion…

A p-n junction, induced in graphene by gating, works to contrast the edge states of electrons and holes on each side of it. In a magnetic field those edge states carry two species of persistent current, which are intimately tied to the…

We consider a single layer of graphene subjected to a magnetic field $H$ applied perpendicular to the layer and an in-plane constant radial electric field $E$. The Dirac equation for this configuration does not admit analytical solutions in…

Chen, Apalkov, and Chakraborty (Phys. Rev. Lett. 98, 186803 (2007)) have computed Fock-Darwin levels of a graphene dot by including only basis states with energies larger than or equal to zero. We show that their results violate the…

We analyze the single particle states at the edges of disordered graphene quantum dots. We show that generic graphene quantum dots support a number of edge states proportional to circumference of the dot over the lattice constant. Our…

The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background…

We consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary conditions are defined by a matrix depending on four real…

The density of states and differential entropy per particle are analyzed for Dirac-like electrons in graphene subjected to a perpendicular magnetic field and an in-plane electric field. For comparison, the derived density of states is…

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…

Within the tight binding approximation, we study the dependence of the electronic band structure and of the optical conductivity of a graphene single layer on the modulus and direction of applied uniaxial strain. While the Dirac cone…

This work presents a novel approach to describe spectral properties of graphene layers with well defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the…

In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…

The "catastrophe" in solving the Dirac equation for an electron in the field of a point electric charge, which emerges for the charge numbers Z > 137, is removed in this work by effective accounting of finite dimensions of nuclei. For this…

We address the question of how the Aharonov-Bohm flux $\Phi_{AB}$ can affect the energy levels of graphene magnetic quantum dots (GMQDs) of radius $R$. To answer this question, we consider GMQDs induced by a magnetic field $B$ and subjected…

Grain boundaries are topological defects that often have a disordered character. Disorder implies that understanding general trends is more important than accurate investigations of individual grain boundaries. Here we present trends in the…