Puzzling superconductivity in strontium ruthenate: Then and now (Brief Review)

Strontium ruthenate is a very interesting low-temperature superconductor with a relatively simple normal state and puzzling superconducting-state properties. Despite over thirty years of intensive research, even the precise symmetry of the order parameter is not known. In this paper, we briefly review key developments, focusing on newer experiments, especially those that challenged the previous understanding that it is a spin-triplet, odd-parity, chiral p-wave superconductor. Since Sr2RuO4 now appears most probably to be a spin-singlet superconductor, we have calculated the Kerr effect for one candidate d-wave pairing state. We find that for the chiral d-wave Eg pairing state, the calculated Hall conductance is non-zero and qualitatively similar to that found earlier under the assumption of a chiral p-wave Eu order parameter. We characterize the Hall conductance in relation to two sum rules, one related to Berry curvatures in the Bogoliubov quasiparticle states, and the other f-sum rule indicating the presence of inter-orbital pairing.