Spin-orbit coupling and spin-triplet pairing symmetry in $\mathrm{Sr_2 Ru O_4}$

TL;DR

This paper investigates how spin-orbit coupling influences the degeneracy and stability of p-wave spin-triplet pairing states in Sr2RuO4, combining theoretical and numerical methods to clarify the pairing symmetry.

Contribution

It provides a comprehensive analysis of SOC effects on pairing symmetry in Sr2RuO4 using Ginzburg-Landau theory, symmetry analysis, and numerical calculations, offering guidance for future research.

Findings

SOC lifts degeneracy among p-wave pairing states

Re-examination of chiral p-wave pairing stability

Symmetry analysis aids future studies

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 $\mathrm{Sr_2 Ru O_4}$, 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 $\mathrm{Sr_2 Ru O_4}$ and can be useful for studying other multi-band spin-triplet superconductors where SOC plays an important role.