Topologically localized insulators

TL;DR

This paper demonstrates that three-dimensional, fully-localized insulators with broken time-reversal symmetry can exhibit multiple topologically distinct phases characterized by integer invariants, with phase transitions linked to system conductivity.

Contribution

It introduces a new classification of localized insulators into topological phases distinguished by integer invariants, expanding understanding of topological matter beyond disorder-free systems.

Findings

Localized insulators can host topologically distinct phases.

Boundary states lead to quantized boundary Hall conductance.

Phase transitions occur when the system becomes conducting.

Abstract

We show that fully-localized, three-dimensional, time-reversal-symmetry-broken insulators do not belong to a single phase of matter but can realize topologically distinct phases that are labelled by integers. The phase transition occurs only when the system becomes conducting at some filling. We find that these novel topological phases are fundamentally distinct from insulators without disorder: they are guaranteed to host delocalized boundary states giving rise to the quantized boundary Hall conductance, whose value is equal to the bulk topological invariant.