Topological Insulators at Strong Disorder

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.