Topology of ultra-localized insulators and superconductors

TL;DR

This paper classifies ultra-localized insulators and superconductors, revealing their unique topological properties and how they differ from conventional topological phases, especially regarding bulk-boundary correspondence and Wannierizability.

Contribution

It provides a comprehensive classification of ultra-localized topological phases across all symmetry classes and dimensions, highlighting phases not captured by existing frameworks.

Findings

Ultra-localized insulators can have distinct topological classifications.

Many ultra-localized phases are not described by known topological insulator classifications.

Certain topological phases require delocalized states and cannot be Wannierized.

Abstract

The topology of an insulator can be defined even when all eigenstates of the system are localized - an extreme case of Anderson insulators that we call ultra-localized. We derive the classification of such ultra-localized insulators in all symmetry classes and dimensions. We clarify their bulk-boundary correspondence and show that ultra-localized systems are in many instances phases of matter not described by the known classification of topological insulators and superconductors. As a consequence, we clarify which conventional topological phases are Wannierizable, and which topological phases cannot exist without delocalized states.