Related papers: Dirac electron in graphene under supersymmetry gen…
A general discussion of graphene in external electromagnetic field is provided. In general, the formulation is not Lorentz invariant because of Zeeman energy. But it can be restored approxiamtely in the case of strong magnetic field, the…
Lattice deformations couple to the low energy electronic excitations of graphene as vector fields similar to the electromagnetic potential \cite{SA02b,VKG10}. The suggestion that certain strain configurations would be able to induce pseudo…
Slowly varying nonuniform strains of non-magnetic wave propagating media with honeycomb symmetry induce an effective- or pseudo-magnetic field, a phenomenon observed first in graphene, and later in photonic crystals and other physical…
This paper is devoted to the construction of semiclassical spectrum and efficient (simple to implement) explicit semiclassical asymptotic eigenfunctions of the Dirac operator for relatively high-energy bound states in graphene in magnetic…
A generalized algebra of noncommutative coordinates and momenta embracing non-Abelian gauge fields is proposed. Through a two-dimensional realization of this algebra for a gauge field including electromagnetic vector potential and two…
We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac…
Investigation of real two-dimensional systems with Dirac-like electronic behavior under the influence of magnetic field is challenging and leads to many interesting physical results. In this paper we study 2D graphene model with a…
Due to Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design…
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…
Electron supercollimation, in which a wavepacket is guided to move undistorted along a selected direction, is a highly desirable property that has yet been realized experimentally. Disorder in general is expected to inhibit…
We show that 2+1 dimensional Dirac oscillators in an external magnetic field is mapped onto the same with reduced angular frequency in absence of magnetic field. This can be used to study the atomic transitions in a radiation field.…
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
Many of the properties of graphene are tied to its lattice structure, allowing for tuning of charge carrier dynamics through mechanical strain. The graphene electro-mechanical coupling yields very large pseudomagnetic fields for small…
Strain engineering of graphene takes advantage of one of the most dramatic responses of Dirac electrons enabling their manipulation via strain-induced pseudo-magnetic fields. Numerous theoretically proposed devices, such as resonant…
Graphene placed in a magnetic field possesses an extremely high mid/far-infrared optical nonlinearity originating from its unusual band structure and selection rules for the optical transitions near the Dirac point. Here we study the linear…
The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly…
After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene.…
We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of…
The relativistic Foldy-Wouthuysen transformation is used for an advanced description of planar graphene electrons in external fields and free (2+1)-space. It is shown that the initial Dirac equation should by based on the usual $(4\times4)$…