Topologically stable gapless phases in nonsymmorphic superconductors

Abstract

We study topological stability of nodes in nonsymmorphic superconductors (SCs). In particular, we demonstrate that line nodes in nonsymmirphic odd-parity SCs are protected by the interplay between topology and nonsymmorphic symmetry. As an example, it is shown that the $E_{2u}$-superconducting state of UPt$_3$ hosts the topologically stable line node at the Brillouin zone face. Our theory indicates that the existence of spin-orbit coupling is essential for protecting such a line node, complementing the Norman's group theory argument. Developing the topological arguments, we also argue generalization to point nodes and to other symmetry cases beyond the group theory arguments.