Extended topological group structure due to average reflection symmetry

TL;DR

This paper extends the topological classification of insulators and superconductors to systems with disorder that preserves average reflection symmetry, revealing an exponential extension of the topological group structure and its physical implications.

Contribution

It introduces a new topological classification framework accounting for average reflection symmetry, expanding the understanding of topological phases in disordered systems.

Findings

Topological group structure is exponentially extended under average reflection symmetry.

Localization-delocalization transitions occur between phases with the same boundary conductance.

Gapless topological defects are stabilized by average reflection symmetry.

Abstract

We extend the single-particle topological classification of insulators and superconductors to include systems in which disorder preserves average reflection symmetry. We show that the topological group structure of bulk Hamiltonians and topological defects is exponentially extended when this additional condition is met, and examine some of its physical consequences. Those include localization-delocalization transitions between topological phases with the same boundary conductance, as well as gapless topological defects stabilized by average reflection symmetry.