Spin-orbital coupling and spin-triplet pairing symmetry in Sr₂RuO₄

Spin-orbital coupling (SOC) plays a crucial role in determining the spin structure of an odd parity pseudospin-triplet Cooper pairing state. We discuss how SOC lifts the degeneracy among different p-wave pseudospin-triplet pairing states in a widely used microscopic model for Sr₂RuO₄ combining a Ginzburg-Landau free energy expansion, a symmetry analysis of the model, and numerical weak-coupling renormalization group, as well as random phase approximation, calculations. These analyses are also 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 Sr₂RuO₄ and can be useful for studying other multi-band spin-triplet superconductors where SOC plays an important role.