A review of some new perspectives on the theory of superconducting Sr₂RuO₄

The nature of the Cooper pairing in the paradigmatic unconventional superconductor Sr₂RuO₄ is an outstanding puzzle in condensed matter physics. Despite the tremendous efforts made in the past twenty-seven years, neither the pairing symmetry nor the underlying pairing mechanism in this material has been understood with clear consensus. This is largely due to the lack of a superconducting order that is capable of interpreting in a coherent manner the numerous essential experimental observations. At this stage, it may be desirable to reexamine our existing theoretical descriptions of superconducting Sr₂RuO₄. This review focuses on several recent developments that may provide some clues for future study. We highlight three separate aspects: 1) any pairing in the E_u symmetry channel, with which the widely discussed chiral p-wave is associated, shall acquire a 3D structure due to spin-orbit entanglement; 2) if the reported Kerr effect is a superconductivity-induced intrinsic bulk response, the superconductivity must either exhibit a chiral character, or be complex mixtures of certain set of helical p-wave pairings; 3) when expressed in a multiorbital basis, the Cooper pairing could acquire numerous exotic forms that are inaccessible in single-orbital descriptions. The implications of each of these new perspectives are briefly discussed in connection with selected experimental phenomena.