Asymmetric transport for magnetic Dirac equations

TL;DR

This paper investigates the quantized and robust asymmetric transport phenomena at interfaces in magnetic Dirac models of graphene, providing explicit formulas and demonstrating stability under various perturbations.

Contribution

It introduces a spectral flow formula for interface conductivity in magnetic Dirac equations and proves its quantization and robustness against perturbations.

Findings

Interface conductivity is quantized.

Transport is robust to defects and field variations.

Explicit spectral flow formula derived.

Abstract

This paper concerns the asymmetric transport associated with a low-energy interface Dirac model of graphene-type materials subject to external magnetic and electric fields. We show that the relevant physical observable, an interface conductivity, is quantized and robust to a large class of perturbations. These include defects that decay along or away from the interface, and sufficiently small or localized changes in the external fields. An explicit formula for the interface conductivity is given by a spectral flow.