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A comprehensive theory of superconductivity in Sr$_2$RuO$_4$ must explainexperiments that suggest even parity superconducting order and others thatsuggest broken time reversal symmetry. Completeness further requires that thetheory applies to Ca$_2$RuO$_4$, a Mott-Hubbard semiconductor that exhibits anunprecedented insulator-to-metal transition driven by very small electricfield, and also by doping with very small concentration of electrons, leadingto 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 metaltransition is distinct from that expected from the simple melting of theMott-Hubbard semiconductor. Rather, the Ru ions occur as low spin Ru$^{4+}$ inthe semiconductor, and as high spin Ru$^{3+}$ in the metal, the driving forcebehind the valence transition being the strong spin-charge coupling andconsequent large ionizaton energy in the low charge state. Metallic andsuperconducting ruthenates are two-component systems in which the half-filledhigh spin Ru$^{3+}$ ions determine the magnetic behavior but not transport,while the charge carriers are entirely on on the layer oxygen ions, which havean average charge -1.5. Spin singlet superconductivity evolves from thecorrelated lattice frustrated 3/4 filled band of layer oxygen ions alone, inagreement with quantum many body calculations that have demonstratedenhancement by electron-electron interactions of superconducting pair-paircorrelations tions uniquely at or very close to this filling [Phys. Rev. B {\bf93}, 165110 and {\bf 93}, 205111]. Several model specific experimentalpredictions are made, including that spin susceptibility due to Ru ions willremain unchanged as Sr$_2$RuO$_4$ is taken through superconducting Tc.

physical review research

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