Related papers: Energy levels of triangular and hexagonal graphene…
We numerically investigate quantum rings in graphene and find that their electronic properties may be strongly influenced by the geometry, the edge symmetries and the structure of the corners. Energy spectra are calculated for different…
The second-order Dirac equation (DE) and its velocity operator of graphene electrons in an electromagnetic field are obtained according to tight-binding k.p method. With extra terms included, they demonstrate the motion of graphene…
Boundaries and edges of a two dimensional system lower its symmetry and are usually regarded, from the point of view of charge transport, as imperfections. Here we present a first study of the behavior of graphene plasmons in a strong…
We present a tight binding theory of the Dirac point resonances due to adsorbed atoms and molecules on an infinite 2D graphene sheet based on the standard tight binding model of the graphene p-band electronic structure and the extended…
The diamagnetism of confined Dirac fermions submitted to a uniform magnetic field in disordered graphene is investigated. The solutions of the energy spectrum are used to discuss the orbital magnetism from a statistical mechanical point of…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
Using the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a nonlinear first-order differential equation from which we can treat both confined-state problems in electron waveguides and…
Various types of topological defects in graphene are considered in the framework of the continuum model for long-wavelength electronic excitations, which is based on the Dirac--Weyl equation. The condition for the electronic wave function…
The fate of the charge-neutral Dirac point in graphene in a high magnetic field $H$ has been investigated at low temperatures ($T\sim$ 0.3 K). In samples with small $V_0$ (the gate voltage needed to access the Dirac point), the resistance…
The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice…
We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are…
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…
We study electron scattering in graphene quantum dots (GQDs) under the combined influence of a magnetic field, an energy gap, and circularly polarized laser irradiation. Using the Floquet approach and the Dirac equation, we derive the…
It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the…
The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected $C^3$-domains with infinite mass boundary conditions. This bound is given in terms of a conformal…
We theoretically consider, comparing with the existing experimental literature, the electrical conductivity of gated monolayer graphene as a function of carrier density, temperature, and disorder in order to assess the prospects of…
We study the low-energy electronic transport across periodic extended defects in graphene. In the continuum low-energy limit, such defects act as infinitesimally thin stripes separating two regions where Dirac Hamiltonian governs the…
By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference…
The excitations in graphene and some other materials are described by two-dimensional massless Dirac equation with applied external potential of some kind. Solutions of this zero energy equation are built analytically for a wide class of…
We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a…