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

TL;DR

This paper introduces an analytical method to solve the Dirac-Weyl equation for graphene electrons under combined electric and magnetic fields, using supersymmetric quantum mechanics, demonstrated with an electric square well example.

Contribution

It presents a novel analytical approach leveraging supersymmetric quantum mechanics to solve for low-energy electron states in graphene under specific field configurations.

Findings

Analytical solutions for Dirac-Weyl in electric/magnetic fields

Decoupling method based on symmetry assumptions

Application to electric square well case

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.