Topological crystalline superconductivity in locally noncentrosymmetric ${\mathrm{CeRh}}_2{\mathrm{As}}_2$

Recent discovery of superconductivity in ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ clarified an unusual $H\text{−}T$ 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 ${\mathbb{Z}}_2$ invariant of glide symmetric and time-reversal symmetry-broken superconductors by the number of Fermi surfaces on a glide invariant line. Next, we conduct 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.

Figure 1

(a) Schematic $H\text{−}T$ phase diagram of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ [72]. The Bardeen-Cooper-Schrieffer state is assumed to be an even-parity superconducting phase, and the high-field phase is supposed to be the pair-density-wave (PDW) state, the main topic in this Letter. (b) Crystal structure of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ generated by vesta [104].

Figure 2

Electronic band structure of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ with spin-orbit coupling calculated by wien2k. (a) The whole bands along symmetric lines. The heavy bands of $\mathrm{Ce}4f$ electrons are seen near the Fermi level. (b) Enlarged view along the $M\text{−}\mathrm{\Gamma }$ line. The bands cross the Fermi level three times. (c) Enlarged view along the $A\text{−}Z$ line. The bands cross the Fermi level four times.

Figure 3

(a) Fermi surfaces of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$. Each Fermi surface is shown in (b)–(d). The Fermi surfaces other than the pockets around the $A$ point in (d) are mainly constituted by $\mathrm{Ce}4f$ electrons. The figures are generated by XCrySDen software [105].

Figure 4

$\left(\overline{1}10\right)$ and $\left(1\overline{1}0\right)$ surface states of (a) $A_{2u}$ and (b) $B_{2u}$ superconducting states at one of the glide-invariant planes, $k_z=0$. The orange (blue) color represents the glide-even (odd) sector. The axis $k_{a^{\prime }}$ corresponds to $k_x+k_y$, and Majorana surface states appear at $k_{a^{\prime }}=0$.