Spin-orbit induced mixed-parity pairing in Sr$_2$RuO$_4$: a self-consistent quantum many-body analysis

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 a pure 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$_4$ such as the weak temperature dependence of the spin susceptibility below $T_c$. However, 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 parity pairing state provides an alternative scenario for understanding the complex phenomena measured in Sr$_2$RuO$_4$.