Spin-orbit coupling and spin-triplet pairing symmetry in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">RuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>
Zhiqiang Wang, Xin Wang, Catherine Kallin
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 ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, 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 ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and can be useful for studying other multiband spin-triplet superconductors where SOC plays an important role.