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Asymmetric transport for magnetic Dirac equations

Solomon Quinn and Guillaume Bal

Vol. 6 (2024), No. 2, 353–377
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.

Keywords
bulk-interface correspondence, Dirac equation, spectral flow, topological insulator
Mathematical Subject Classification
Primary: 35P15
Secondary: 35J46, 81Q15
Milestones
Received: 13 January 2023
Revised: 10 September 2023
Accepted: 2 January 2024
Published: 16 May 2024
Authors
Solomon Quinn
School of Mathematics
University of Minnesota
Minneapolis, MN
United States
Guillaume Bal
Departments of Statistics and Mathematics
University of Chicago
Chicago, IL
United States