Spin-orbit induced mixed-parity pairing in Sr${}_2$RuO${}_4$: a quantum many-body calculation

The unusual superconducting state in Sr${}_2$RuO${}_4$ has long been viewed as being analogous to a superfluid state in liquid ${}^3$He. Nevertheless, calculations based on this odd-parity state are presently unable to completely reconcile the properties of Sr${}_2$RuO${}_4$. Using a self-consistent quantum many-body scheme that employs realistic parameters, we are able to model several signature properties of the normal and superconducting states of Sr${}_2$RuO${}_4$. We find that the dominant component of the model superconducting state is of even parity and closely related to superconducting state for the high-$T_c$ cuprates although a smaller odd-parity component is induced by spin-orbit coupling. This mixed pairing state gives a more complete representation of the complex phenomena measured in Sr${}_2$RuO${}_4$.