Graphene Dirac fermions in one-dimensional inhomogeneous field profiles: Transforming magnetic to electric field

TL;DR

This paper demonstrates a transformation linking magnetic and electric field effects in graphene, revealing new insights into carrier velocity, Landau levels, and electron transmission, with implications for device design.

Contribution

It introduces a novel transformation mapping magnetic field effects to electric field effects in graphene, providing new analytical tools and understanding.

Findings

Carrier velocity is isotropically reduced under periodic magnetic fields.

Landau level bandwidth decreases with increasing average magnetic flux.

Electron transmission probabilities through magnetic barriers can be derived from electrostatic barriers.

Abstract

We show that the low-energy electronic structure of graphene under a one-dimensional inhomogeneous magnetic field can be mapped into that of graphene under an electric field or vice versa. As a direct application of this transformation, we find that the carrier velocity in graphene is isotropically reduced under magnetic fields periodic along one direction with zero average flux. This counterintuitive renormalization has its origin in the pseudospin nature of graphene electronic states and is robust against disorder. In magnetic graphene superlattices with a finite average flux, the Landau level bandwidth at high fields exhibits an unconventional behavior of decreasing with increasing strength of the average magnetic field due to the linear energy dispersion of graphene. As another application of our transformation relation, we show that the transmission probabilities of an electron through a magnetic barrier in graphene can directly be obtained from those through an electrostatic barrier or vice versa.