Parity games and mystery order in a heavy-fermion superconductor

Heavy fermion superconductors are a fascinating class of materials.These unconventional superconductors form from heavy quasiparticles that originate from localized f-electrons liberated into a Fermi sea.Recently two new members of this materials class, UTe 2 and CeRh 2 As 2 , have generated tremendous interest.UTe 2 was the emphasis of a commentary by Piers Coleman and Tamaghna Hazra [1].The interest in CeRh 2 As 2 stems from its superconducting temperature-magnetic field phase diagram when a magnetic field is applied along the c-axis in this tetragonal material (see Fig. 1) [2].This phase diagram has two notable features.The first is a field induced first order transition between two superconducting phases (called SC1 and SC2).The second is a record high value of H c2 /T c , where H c2 is the upper critical field and T c is the superconducting transition temperature.This record value suggests a natural protection of superconductivity against a c-axis field.The observed behavior has been attributed to the crystal structure.There are two inequivalent Ce atoms per unit cell and there is no inversion symmetry at either Ce atom.However, the two inequivalent Ce atoms are inversion symmetry partners of each other, so there is a global inversion symmetry.The inequivalent Ce atoms each form a square lattice.The interpretation of the superconducting phase diagram is that in each Ce square lattice layer, there are local interactions that give rise to a spin-singlet superconducting state (for example s-wave or d-wave) [2, 3].As shown in Fig. 2, the inversion center between the two Ce layers naturally allows for two superconducting states: an even parity state where the 1