Bound states for massive Dirac fermions in graphene in a magnetic step field

TL;DR

This paper derives an analytical relation for the spectrum of massive Dirac fermions in graphene under a step magnetic field, revealing how tuning the mass term controls edge state velocities.

Contribution

It provides a universal analytical relation linking bandwidths and velocities of edge modes in graphene with inhomogeneous magnetic fields.

Findings

Analytical spectrum relation for massive Dirac fermions in magnetic steps

Control of edge state velocities via mass term tuning

Universal relation between bandwidths and propagating velocities

Abstract

We calculate the spectrum of massive Dirac fermions in graphene in the presence of an inhomogeneous magnetic field modeled by a step function. We find an analytical universal relation between the bandwidths and the propagating velocities of the modes at the border of the magnetic region, showing how by tuning the mass term one can control the speed of these traveling edge states.