Scattering theory of topologically protected edge transport

TL;DR

This paper introduces a scattering theory framework to analyze asymmetric edge transport in two-dimensional topological insulators, linking physical observables to scattering matrices and demonstrating stability under perturbations.

Contribution

It develops a novel scattering theory for topological insulator interfaces, connecting transport asymmetry to scattering matrices and applying it to perturbed Dirac systems.

Findings

Transport asymmetry is expressed as a difference of transmission coefficients.

The observable related to asymmetry is stable against perturbations.

The theory is applied to systems with perturbed Dirac equations and domain walls.

Abstract

This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a limiting absorption principle and construct a generalized eigenfunction expansion for perturbed systems. We then relate a physical observable quantifying the transport asymmetry to the scattering matrix associated to the generalized eigenfunctions. In particular, we show that the observable is concretely expressed as a difference of transmission coefficients and is stable against perturbations. We apply the theory to systems of perturbed Dirac equations with asymptotically linear domain wall.