Related papers: 1-D Dirac Equation, Klein Paradox and Graphene
We obtain exact solutions of the (1+1) dimensional Klein Gordon equation with linear vector and scalar potentials in the presence of a minimal length. Algebraic approach to the problem has also been studied.
The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the…
We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $\gamma^0 f(x,t) - i \mu \gamma^0 \Psi$, where both $f, \{f_j = r_i e^{i…
Graphene is a zero-gap semiconductor, where the electrons propagating inside are described by the ultra-relativistic Dirac equation normally reserved for very high energy massless particles. In this work, we show that graphene under a…
The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the…
The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from the behavior of non-relativistic electrons seen in traditional atomic and impurity systems. Surprisingly, many key theoretical predictions for…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…
We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to the one second order differential equation. We obtained the…
The mode-dependent transmission of relativistic ballistic massless Dirac fermion through a graphene based double barrier structure is being investigated for various barrier parameters. We compare our results with already published work and…
Graphene is characterized by chiral electronic excitations. As such it provides a perfect testing ground for the production of Klein pairs (electron/holes). If confirmed, the standard results for barrier phenomena must be reconsidered with,…
We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit…
We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.
This paper examines the Foldy-Wouthuysen and Feynman-Gell-Mann representations of the Dirac equation. The analysis is conducted for electrons and positrons interacting with electromagnetic fields. Versions of quantum electrodynamics are…
A method is derived to solve the massless Dirac-Weyl equation describing electron transport in a mono-layer of graphene with a scalar potential barrier U(x,t), homogeneous in the y-direction, of arbitrary x- and time dependence. Resonant…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated…
Solutions of the Dirac equation with spin and pseudospin symmetry for the scalar and vector trigonometric scarf potential in $D$-dimensions within the framework of an approximation scheme to the centrifugal barrier are obtained. The energy…
We compare two different solutions of the Dirac equation in (1+1) dimensions. One solution is for a fermion in the presence of an electric potential and the other is for a fermion in the presence of a pseudoscalar potential. It is shown…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
We study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming…