Z4 Topological Superconductivity in UCoGe

Topological nonsymmorphic crystalline superconductivity (TNCS) is an intriguing phase of matter, offering a platform to study the interplay between topology, superconductivity, and nonsymmorphic crystalline symmetries. Interestingly, some of TNCSs are classified into Z(4) topological phases, which have unique surface states referred to as a Mobius strip or an hourglass, and they have not been achieved in symmorphic superconductors. However, material realization of Z(4) TNCS has never been known, to the best of our knowledge. Here, we propose that the paramagnetic superconducting phase of UCoGe under pressure is a promising candidate of Z(4)-nontrivial TNCS enriched by glide symmetry. We evaluate Z(4) invariants of UCoGe by deriving the formulas relating Z(4) invariants to the topology of Fermi surfaces. Applying the formulas and previous ab initio calculations, we clarify that three odd-parity representations out of four are Z(4)-nontrivial TNCS, whereas the other is also Z(4)-nontrivial TNCS. We also discuss possible Z(4) TNCS in CrAs and related materials.