Topological Nonsymmorphic Crystalline Superconductors

TL;DR

This paper introduces a new class of topological superconductors protected by nonsymmorphic crystalline symmetry, specifically glide symmetry, and extends the classification to include time-reversal symmetric classes in two dimensions.

Contribution

It constructs explicit models for topological nonsymmorphic crystalline superconductors and generalizes their classification to additional symmetry classes.

Findings

Majorana zero modes are protected by glide symmetry.

The classification is extended to DIII and BDI classes in 2D.

Provides guidance for discovering new materials with nonsymmorphic structures.

Abstract

Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes", at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed "topological nonsymmorphic crystalline superconductors". We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide symmetry. Furthermore, we generalize the classification of topological nonsymmorphic crystalline superconductors to the classes with time reversal symmetry, including the DIII and BDI classes, in two dimensions. Our theory provides a guidance to search for new topological superconducting materials with nonsymmorphic crystal structures.