An analytical solution for the graphene electronic spectrum in the presence of external fields and confinement potential

Abstract

An algebraic solution of [Formula: see text]-dimensional Dirac equation describing the massless Dirac fermions in the presence of both magnetic field perpendicular to the graphene plane and in-plane homogeneous electric field together with a quadratic confinement potential is investigated. The associated energy eigenvalues are obtained within the framework of unitary transformation scheme. It is shown that the decreasing quadratic confinement potential strength leads to the enhancement of the Landau levels.