Kramers' degenerate magnetism and superconductivity

Motivated by the recent discovery of odd-parity multipolar antiferromagnetic order in CeRh2As2, we examine the coexistence of such translation invariant Kramers' degenerate magnetic states and superconductivity. We show that the presence of such magnetic states generically suppresses superconductivity, whether it be spinsinglet or spin-triplet, unless the magnetic state drives a symmetry-required pair density wave superconducting order. We apply our results to CeRh2As2, where no pair density wave order appears, and to the loop current order in the cuprates, where such pair density wave superconductivity must appear together with Bogoliubov Fermi surfaces. In the former case, we explain why superconductivity is not suppressed.