Quantum Many-Body Calculation of Mixed-Parity Pairing in the ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ Superconductor Induced by Spin-Orbit Coupling

The unusual superconducting state in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ has long been viewed as being analogous to a superfluid state in liquid ${}^3\mathrm{He}$. Nevertheless, calculations based on this odd-parity state are presently unable to completely reconcile the properties of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. 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 ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. 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 ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

Figure 1

Comparison of low energy band structure derived from FLEX calculations (symbols) and LDA (solid lines) along the indicated symmetry directions. The vertical lines through each point correspond to the inverse lifetime of the state. There is a significant renormalization of each band, with the $\gamma$ band showing the strongest renormalization along $\Gamma \mathrm{\text{−}}M$.

Figure 2

Quasiparticle spectrum along the $\Gamma \mathrm{\text{−}}M$ direction for $T<T_c$. The usual signature of a superconducting gap appears in the $\gamma$ band. There is no evidence for a smaller gap forming in the $\beta$ band along this cut to within the momentum resolution of the calculation.

Figure 3

Temperature dependence of the Pauli spin susceptibility ${\chi }_{\mathrm{sp}}$, for zero and finite spin-orbit coupling constant $\lambda$. For $\lambda =0$ the equal in-plane and out-of-plane components are suppressed by the superconducting transition. In contrast, for $\lambda =70\mathrm{meV}$, both the in-plane and out-of-plane components are suppressed by less than 10% for $T<T_c$.