Scattering theory of topological insulators and superconductors

TL;DR

This paper introduces a scattering matrix-based method to compute topological invariants of insulators and superconductors using only Fermi level data, enhancing efficiency and applicability to disordered systems.

Contribution

It presents a novel approach to determine topological invariants solely from scattering matrices at the Fermi level, bypassing the need for full spectral information.

Findings

Method efficiently computes topological invariants from scattering data.

Approach is well-suited for disordered systems.

Connects topological invariants to measurable transport properties.

Abstract

The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require knowledge of all states below the Fermi energy. Here, we propose a way to calculate the topological invariant employing solely its scattering matrix at the Fermi level without knowledge of the full spectrum. Since the approach based on scattering matrices requires much less information than the Hamiltonian-based approaches (surface versus bulk), it is numerically more efficient. In particular, is better-suited for studying disordered systems. Moreover, it directly connects the topological invariant to transport properties potentially providing a new way to probe topological phases.