Efficient method to compute $\mathbb{Z}_4$-indices with glide symmetry and applications to M\"obius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$

TL;DR

This paper introduces an efficient computational method for $ ext{Z}_4$-indices in glide-symmetric topological phases, enabling detailed analysis of M"obius materials like CeNiSn and UCoGe, revealing new topological features and gapless excitations.

Contribution

The authors develop a direct lattice-based method to evaluate $ ext{Z}_4$-indices, simplifying the analysis of glide-symmetric topological phases and applying it to real materials.

Findings

UCoGe exhibits strong M"obius superconductivity in certain representations.

Phase diagrams reveal topological gapless excitations protected by glide symmetry.

Doping holes induces observable gapless excitations in superconducting phases.

Abstract

We propose an efficient method to numerically evaluate $\mathbb{Z}_4$-indices of M\"obius/hourglass topological phases with glide symmetry. Our method directly provides $\mathbb{Z}_4$-indices in the lattice Brillouin zone while the existing method requires careful observations of momentum dependent Wannier charge centers. As applications, we perform systematic computation of $\mathbb{Z}_4$-indices for M\"obius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$. In particular, our analysis elucidates that $\mathrm{UCoGe}$ shows strong M\"obius superconductivity for the $A_u$- or $B_{3u}$-representation whose topology has not been fully characterized. Furthermore, obtained phase diagrams reveal novel topological gapless excitations in the bulk which are protected by nonsymmorphic glide symmetry. We observe these gapless excitations with glide symmetry by doping holes into the superconducting phase of the $B_{1u}$- or $B_{3u}$-representation.