Symmetry Properties of Superconducting Order Parameter in Sr₂RuO₄: A Brief Review

Soon after the discovery of superconductivity in Sr₂RuO₄ (SRO) a quarter-century ago, it was conjectured that its order parameter (OP) has a form similar to that realized in the superfluid phases of 3-He, namely, odd parity and spin triplet. While the chiral p-wave pairing believed to be realized in the A phase of that system was favored by several early experiments, in particular, the muon spin rotation and the Knight shift measurements published in 1998, the original Knight shift result was called into question in early 2019, raising the question as to whether the “chiral p-wave”, or even the spin-triplet pairing itself, is indeed realized in SRO. In this brief pedagogical review, we will address this question by counterposing the currently accepted results of Knight shift, polarized neutron scattering, spin counterflow half-quantum vortex (HQV), and Josephson experiments, which probe the spin and orbital parts of the OP, respectively, with predictions made both by standard BCS theory and by more general arguments based only on (1) the symmetry of the Hamiltonian including the spin-orbital terms, (2) thermodynamics, and (3) the qualitative experimental features of the material. In the hope of enhancing readers’ intuitive grasp of these arguments, we introduce a notation for triplet states alternative to the more popular “d-vector” one which we believe well suited to SRO. We conclude that the most recent Knight shift and polarized neutron scattering experiments do not exclude in the bulk the odd-parity, spin-triplet “helical” states allowed by the symmetry group of SRO but do exclude the “chiral p-wave”, Γ5− state. On the other hand, the Josephson and in-plane-magnetic-field stabilized HQV experiments showed that the pairing symmetry in SRO cannot be of the even-parity, spin-singlet type, and furthermore, that in the surface region or in samples of mesoscopic size the d-vector must be along the c axis, thus excluding all bulk p-wave states except Γ5−. Possible resolution of this rather glaring prima facie contradiction is discussed, taking into account implications of other important experiments on SRO, including that of the muon spin rotation, which are touched upon briefly only towards the end of this article.