Recent discovery of superconductivity in ${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$ clarified an unusual $H\text{\u2212}T$ phase diagram with two superconducting phases [Khim *et al.* Science, **373**, 1012 (2021)]. The experimental observation has been interpreted based on the even-odd parity transition characteristic of locally noncentrosymmetric superconductors. Indeed, inversion symmetry is locally broken at the Ce site, and ${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$ molds a 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 like spin-triplet superconductors. In this Letter, we first derive the formula expressing the ${{Z}}_{2}$ invariant of glide symmetric and time-reversal symmetry-broken superconductors by the number of Fermi surfaces on a glide invariant line. Next, we conduct first-principles calculations for the electronic structure of ${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$. Combining the results, we show that the field-induced odd-parity superconducting phase of ${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$ is a platform of topological crystalline superconductivity protected by nonsymmorphic glide symmetry and accompanied by boundary Majorana fermions.

nogaki.kosuke.83v@st.kyoto-u.ac.jp

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