Sr$_2$RuO$_4$, like doped cuprates and barium bismuthate, is a negative charge-transfer gap even parity superconductor with $\frac{3}{4}$-filled oxygen band

A comprehensive theory of superconductivity in Sr$_2$RuO$_4$ must explain experiments that suggest even parity superconducting order and others that suggest broken time reversal symmetry. Completeness further requires that the theory applies to Ca$_2$RuO$_4$, a Mott-Hubbard semiconductor that exhibits an unprecedented insulator-to-metal transition driven by very small electric field, and also by doping with very small concentration of electrons, leading to a metallic state proximate to ferromagnetism. A valence transition model, previously proposed for superconducting cuprates [Phys. Rev. B {\bf 98}, 205153] is extended to Sr$_2$RuO$_4$ and Ca$_2$RuO$_4$. The insulator to metal transition is distinct from that expected from the simple melting of the Mott-Hubbard semiconductor. Rather, the Ru ions occur as low spin Ru$^{4+}$ in the semiconductor, and as high spin Ru$^{3+}$ in the metal, the driving force behind the valence transition being the strong spin-charge coupling and consequent large ionizaton energy in the low charge state. Metallic and superconducting ruthenates are two-component systems in which the half-filled high spin Ru$^{3+}$ ions determine the magnetic behavior but not transport, while the charge carriers are entirely on on the layer oxygen ions, which have an average charge -1.5. Spin singlet superconductivity evolves from the correlated lattice frustrated 3/4 filled band of layer oxygen ions alone, in agreement with quantum many body calculations that have demonstrated enhancement by electron-electron interactions of superconducting pair-pair correlations tions uniquely at or very close to this filling [Phys. Rev. B {\bf 93}, 165110 and {\bf 93}, 205111]. Several model specific experimental predictions are made, including that spin susceptibility due to Ru ions will remain unchanged as Sr$_2$RuO$_4$ is taken through superconducting Tc.

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