Scattering theory of topologically protected edge transport

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.