Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors

TL;DR

This paper classifies symmetry-protected line nodes in crystalline superconductors and reveals new types of Majorana flat bands, including those in antiferromagnetic superconductors, by linking group theory and topology.

Contribution

It extends the understanding of Majorana flat bands to all symmetry-protected line nodes, including non-symmorphic and magnetic cases, establishing a comprehensive classification framework.

Findings

Classified all possible line-node-induced Majorana flat bands.

Identified new Majorana flat bands in antiferromagnetic superconductors.

Linked group theoretical and topological classifications for superconducting line nodes.

Abstract

Line nodes in the superconducting gap are known to be a source of Majorana flat bands (MFBs) in time-reversal-invariant superconductors (SCs). Here, we extend this relation to all symmetry-protected line nodes where an additional constraint arising from a symmetry of the crystal destabilizes or hides the existence of MFBs. By establishing a one-to-one correspondence between group theoretical and topological classifications, we are able to classify the possible line-node-induced MFBs, including cases with (magnetic) non-symmorphic space groups. Our theoretical analysis reveals a new type of MFB, i.e., MFBs in antiferromagnetic SCs.