Non-symmorphic symmetry and field-driven odd-parity pairing in CeRh2As2

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, to appear in Science]. Here we demonstrate that the P4/nmm non-symmorphic crystal structure of CeRh$_2$As$_2$ is essential to enable the even- to odd-parity transition. The non-symmorphic symmetry ensures the existence of large spin-orbit interactions near the Brillouin zone boundaries, which naturally leads to the near-degeneracy of the even- and odd-parity channels. We illustrate our theory using a DFT-inspired model of the band structure. Finally, we comment on the relevance of our theory to FeSe, which crystallizes in the same structure.