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

The nature of the Cooper pairing in paradigmatic unconventional superconductor Sr$_2$RuO$_4$ is an outstanding puzzle condensed matter physics. Despite tremendous efforts made past twenty-seven years, neither symmetry nor underlying mechanism this material has been understood with clear consensus. This largely due to lack a superconducting order that capable interpreting coherent manner numerous essential experimental observations. At stage, it may be desirable reexamine existing theoretical descriptions Sr$_2$RuO$_4$. review focuses on several recent developments provide some clues for future study. We highlight three separate aspects: 1) any $E_u$ channel, which widely discussed chiral p-wave associated, shall acquire 3D structure spin-orbit entanglement; 2) if reported Kerr effect superconductivity-induced intrinsic bulk response, superconductivity must either exhibit character, or complex mixtures certain set helical pairings; 3) when expressed multiorbital basis, could exotic forms are inaccessible single-orbital descriptions. implications each these new perspectives briefly connection selected phenomena.