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 TNCS are classified into Z4 topological phases, which have unique surface states referred to as a M\"obius strip or an hourglass, and have not been achieved in symmorphic superconductors. However, material realization of Z4 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 Z4-nontrivial TNCS enriched by glide symmetry. We evaluate Z4 invariants of UCoGe by deriving the formulas relating Z4 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 Z4-nontrivial TNCS, while the other is also Z2-nontrivial TNCS. We also discuss possible Z4 TNCS in CrAs and related materials.
@article{arxiv.1803.07786,
title = {$Z_4$ Topological Superconductivity in UCoGe},
author = {Akito Daido and Tsuneya Yoshida and Youichi Yanase},
journal= {arXiv preprint arXiv:1803.07786},
year = {2019}
}