Topological Insulators at Strong Disorder

TL;DR

This paper rigorously characterizes topological insulators under weak and strong disorder, proving their boundary spectrum immunity to localization for a significant portion of the classification, advancing theoretical understanding.

Contribution

It provides a rigorous proof of the boundary spectrum immunity property of topological insulators in both weak and strong disorder regimes, covering over half of the classification table.

Findings

Boundary spectrum immune to Anderson localization

Proven under relevant conditions for many topological classes

Advances theoretical understanding of disordered topological phases

Abstract

Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the rigorous characterization of these materials in the regime of weak and strong disorder. In particular, the defining property is rigorously proven under certain relevant conditions, for more than half of the classification table of topological insulators.