Related papers: Spectrally isomorphic Dirac systems: graphene in e…
We study the role of long-range electron-electron interactions in a system of two-dimensional anisotropic Dirac fermions, which naturally appear in uniaxially strained graphene, graphene in external potentials, some strongly anisotropic…
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 present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued self-adjoint operator, which is also…
Electronic properties of two-dimensional allotropes of carbon, such as graphene and its bilayer, multi-layer epitaxial graphene, few-layer Bernal-stacked graphene, as well as of three-dimensional bulk graphite are reviewed from the…
We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with an hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum…
We show that the low-energy electronic structure of graphene under a one-dimensional inhomogeneous magnetic field can be mapped into that of graphene under an electric field or vice versa. As a direct application of this transformation, we…
The occurrence of Landau levels in quantum mechanics when a charged particle is subjected to a uniform magnetic field is well known. Considering the recent interest in the electronic properties of graphene, which admits a dispersion…
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…
By solving two-component spinor equation for massless Dirac Fermions, we show that graphene under a periodic external magnetic field exhibits a unique energy spectrum: At low energies, Dirac Fermions are localized inside the magnetic region…
We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy…
We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B} = \widetilde{\mathcal{B}}(x,\lambda) \hat{e}_z$ for which the massless Dirac electron possesses exact solution. The…
The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $\psi$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $\omega$, respectively. This theory is connected to…
The behaviour of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, where two one-dimensional Schr\"{o}dinger Hamiltonians $H^{\pm}$ are…
In this paper, a simple method is proposed to get analytical solutions (or with the help of a finite numerical calculations) of the Dirac-Weyl equation for low energy electrons in graphene in the presence of certain electric and magnetic…
The present article discusses magnetic confinement of the Dirac excitations in graphene in presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to $1/r$ is…
A method to construct non-Dirac-hermitian supersymmetric quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations…
An exact mapping of the tight-binding Hamiltonian for a graphene's nanoribbon under any armchair uniaxial strain into an effective one-dimensional system is presented. As an application, for a periodic modulation we have found a gap opening…
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…
This work analyzes monolayer graphene in external electromagnetic fields, which is described by the Dirac equation with minimal coupling. Supersymmetric quantum mechanics allows building new Dirac equations with modified magnetic fields.…
We investigate the notion of subsystem in the framework of spectral triple as a generalized notion of noncommutative submanifold. In the case of manifolds, we consider several conditions on Dirac operators which turn embedded submanifolds…