Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries

TL;DR

This paper explores how nonsymmorphic symmetries like glide planes can protect topological phases in insulators and superconductors, revealing quantized responses and connecting to measurable physical properties.

Contribution

It demonstrates that glide symmetries lead to quantized magnetoelectric polarizability and extends the concept to superconductors, linking bulk invariants to surface responses.

Findings

Glide symmetry induces quantized magnetoelectric polarizability.

Quantization of polarizability extends to any orientation-reversing space group.

Constructs examples of glide protected topological superconductors with measurable surface responses.

Abstract

In this work we consider whether nonsymmorphic symmetries such as a glide plane can protect the existence of topological crystalline insulators and superconductors in three dimensions. In analogy to time-reversal symmetric insulators, we show that the presence of a glide gives rise to a quantized magnetoelectric polarizability, which we compute explicitly through the Chern-Simons 3-form of the bulk wave functions for a glide symmetric model. Our approach provides a measurable property for this insulator and naturally explains the connection with mirror symmetry protected insulators and the recently proposed $Z_2$ index for this phase. More generally, we prove that the magnetoelectric polarizability becomes quantized with any orientation-reversing space group symmetry. We also construct analogous examples of glide protected topological crystalline superconductors in classes D and C and discuss how bulk invariants are related to quantized surface thermal-Hall and spin-Hall responses.