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Non-symmorphic symmetry and field-driven odd-parity pairing in CeRh$_2$As$_2$

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 Added by Daniel F. Agterberg
 Publication date 2021
  fields Physics
and research's language is English




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Recently, evidence has emerged for a field-induced even- to odd-parity superconducting phase transition in CeRh$_2$As$_2$ [S. Khim {it et al.}, arXiv:2101.09522]. Here we argue that the $P4/nmm$ non-symmorphic crystal structure of CeRh$_2$As$_2$ plays a central role in enabling this transition. Specifically, the non-symmorphic symmetries enforce an unusual spin structure near Brillouin zone boundaries that ensures large spin-orbit interactions in these regions of momentum space. This enables a high-temperature field-induced even- to odd-parity transition. We further provide an explicit illustration of the robustness of a field induced odd-parity state within a DFT-inspired model of the superconducting state that includes Fermi surfaces located about a Dirac line at the zone boundary and also about the zone center. Finally, we comment on the relevance of our results to superconducting FeSe, which also crystallizes in a $P4/nmm$ structure.



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We report the discovery of two-phase unconventional superconductivity in CeRh$_2$As$_2$. Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 T, remarkable in a material whose transition temperature is 0.26 K. Furthermore, a $c$-axis field drives a transition between two different superconducting phases. In spite of the fact that CeRh$_2$As$_2$ is globally centrosymmetric, we show that local inversion-symmetry breaking at the Ce sites enables Rashba spin-orbit coupling to play a key role in the underlying physics. More detailed analysis identifies the transition from the low- to high-field states to be associated with one between states of even and odd parity.
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.
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