Statistical Topological Insulators

TL;DR

This paper introduces a new class of topological insulators, called statistical topological insulators, characterized by gapless surface states protected by ensemble symmetries, with implications for higher-dimensional topological phases.

Contribution

The authors define statistical topological insulators, prove their topological nature via a $$ invariant, and show their relation to conventional topological insulators across dimensions.

Findings

Statistical topological insulators are protected by ensemble invariance.

They are characterized by a $$ topological invariant.

Numerical simulations confirm the theoretical predictions.

Abstract

We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these insulators are topological, and are protected by a $\mathbb{Z}_2$ invariant. Finally, we prove that every topological insulator gives rise to an infinite number of classes of statistical topological insulators in higher dimensions. Our conclusions are confirmed by numerical simulations.