Spin-orbit coupling and spin-triplet pairing symmetry in $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$

Abstract

Spin-orbit coupling (SOC) plays a crucial role in determining the spin structure of an odd parity psedospin-triplet Cooper pairing state. Here, we present a thorough study of how SOC lifts the degeneracy among different p-wave pseudospin-triplet pairing states in a widely used microscopic model for $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$, combining a Ginzburg-Landau (GL) free energy expansion, a symmetry analysis of the model, and numerical weak-coupling renormalization group (RG) and random phase approximation (RPA) calculations. These analyses are then used to critically re-examine previous numerical results on the stability of chiral p-wave pairing. The symmetry analysis can serve as a guide for future studies, especially numerical calculations, on the pairing instability in $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$ and can be useful for studying other multi-band spin-triplet superconductors where SOC plays an important role.

13 pages, 7 figures; a discussion on time reversal breaking and ultrasound experiments is added to the conclusion section; published version with other minor changes