Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well

Abstract

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 fields. In order to decouple the Dirac-Weyl equation we have assumed a displacement symmetry of the system along a direction and some conditions on the magnetic and electric fields. The resulting equations have the natural form to apply the technique of supersymmetric quantum mechanics. The example of an electric well with square profile is worked out in detail to illustrate some of the most interesting features of this procedure.

15 pages, 6 figures

References in corpus (18)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Andreev reflection and Klein tunneling in graphene
• Novel electric field effects on Landau levels in Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Electrostatic confinement of electrons in an integrable graphene quantum dot
• Electrostatically confined monolayer graphene quantum dots with orbital and valley splittings
• Two-dimensional Dirac particles in a Pöschl-Teller waveguide
• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• On zero energy states in graphene
• Influence of electric and magnetic fields and $\sigma$-edge bands on the electronic and optical spectra of graphene nanoribbons
• Electronic transport in two-dimensional strained Dirac materials under multi-step Fermi velocity barrier: transfer matrix method for supersymmetric systems
• Coherent states for graphene under the interaction of crossed electric and magnetic fields
• Confinement and edge effects on atomic collapse in graphene nanoribbons
• Complex Supersymmetry in Graphene
• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation
• Massive and massless two-dimensional Dirac particles in electric quantum dots

Cited by in corpus (2)

• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions