Scattering in one-dimensional heterostructures described by the Dirac equation

TL;DR

This paper analyzes electronic transport in one-dimensional heterostructures governed by the Dirac equation, revealing how velocity and mass variations affect backscattering, with implications for graphene-based systems.

Contribution

It generalizes the Dirac Hamiltonian for position-dependent velocity and mass, providing exact solutions and insights into backscattering phenomena in heterostructures.

Findings

No backscattering occurs with velocity profiles.

Mass profiles induce backscattering, less so with linear profiles.

Results are relevant for graphene heterostructure studies.

Abstract

We consider electronic transport accross one-dimensional heterostructures described by the Dirac equation. We discuss the cases where both the velocity and the mass are position dependent. We show how to generalize the Dirac Hamiltonian in order to obtain a Hermitian problem for spatial dependent velocity. We solve exactly the case where the position dependence of both velocity and mass is linear. In the case of velocity profiles, it is shown that there is no backscattering of Dirac electrons. In the case of the mass profile backscattering exists. In this case, it is shown that the linear mass profile induces less backscattering than the abrupt step-like profile. Our results are a first step to the study of similar problems in graphene.