Topological crystalline superconductivity in locally noncentrosymmetric CeRh$_2$As$_2$

TL;DR

This paper demonstrates that CeRh$_2$As$_2$ exhibits topological crystalline superconductivity protected by glide symmetry, with the odd-parity phase hosting boundary Majorana fermions, based on symmetry analysis and first-principles calculations.

Contribution

The study derives a formula for the $ ext{Z}_2$ invariant in glide symmetric superconductors and applies it to CeRh$_2$As$_2$, revealing its topological nature.

Findings

CeRh$_2$As$_2$'s odd-parity phase is topologically nontrivial.

The boundary hosts Majorana fermions due to glide symmetry.

First-principles calculations support the topological interpretation.

Abstract

Recent discovery of superconductivity in CeRh$_2$As$_2$ clarified an unusual $H$-$T$ phase diagram with two superconducting phases [Khim et al. arXiv:2101.09522]. The experimental observation has been interpreted based on the even-odd parity transition characteristic of locally noncentrosymmetric superconductors. Indeed, the inversion symmetry is locally broken at the Ce site, and CeRh$_2$As$_2$ molds a new class of exotic superconductors. The low-temperature and high-field superconducting phase is a candidate for the odd-parity pair-density-wave state, suggesting a possibility of topological superconductivity as spin-triplet superconductors are. In this paper, we first derive the formula expressing the $\mathbb{Z}_2$ invariant of glide symmetric and time-reversal symmetry broken superconductors by the number of Fermi surfaces on a glide invariant line. Next, we conduct a first-principles calculation for the electronic structure of CeRh$_2$As$_2$. Combining the results, we show that the field-induced odd-parity superconducting phase of CeRh$_2$As$_2$ is a platform of topological crystalline superconductivity protected by the nonsymmorphic glide symmetry and accompanied by boundary Majorana fermions.