Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields

TL;DR

This paper provides an exact algebraic method to solve for the eigenvalues and eigenfunctions of a graphene layer subjected to transverse electric and perpendicular magnetic fields, revealing that eigenstates can be expressed as coherent states.

Contribution

It introduces a novel algebraic approach to solve the quantum problem of graphene in combined electric and magnetic fields, with eigenstates expressed as coherent states.

Findings

Eigenvalues and eigenfunctions obtained exactly.

Eigenstates can be represented as coherent states.

Method applicable to similar quantum systems.

Abstract

We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigen-values and the eigen-functions of the graphene plane. It is shown that the eigen-states of the problem can be casted in terms of coherent states, which appears in a natural way from the formalism.