Quantization of Topological Invariants under Symmetry-Breaking Disorder

TL;DR

This paper demonstrates that topological invariants like electric polarization and magneto-electric response remain quantized even when disorder breaks symmetries locally but restores them on average, supported by rigorous analysis and numerical evidence.

Contribution

It provides a rigorous proof that symmetry-stabilized topological invariants retain their quantization under symmetry-breaking disorder that is statistically symmetric.

Findings

Quantization persists under symmetry-breaking disorder.

Numerical calculations confirm theoretical predictions.

Topological invariants are robust to certain types of disorder.

Abstract

In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without time-reversal symmetry and the isotropic magneto-electric response function of time-reversal symmetric insulators are known to be topological invariants displaying an exact $\mathbb Z_2$ quantization. This quantization is stabilized by the symmetries. In the present work, we investigate the fate of such symmetry-stabilized topological invariants in the presence of a disorder which breaks the symmetries but restores them on average. Using a rigorous analysis, we conclude that the strict quantization still holds in these conditions. Numerical calculations confirm this prediction.