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.

arXiv comment13 pages, 7 figures; a discussion on time reversal breaking and ultrasound experiments is added to the conclusion section; published version with other minor changes

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• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• divERGe implements various Exact Renormalization Group examples
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• A microscopic Ginzburg--Landau theory and singlet ordering in Sr${}_2$RuO${}_4$
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• Hidden anomalous Hall effect in Sr${}_2$RuO${}_4$ with chiral superconductivity dominated by the Ru $d_{xy}$ orbital
• Multipole-fluctuation pairing mechanism of $d_{x^2-y^2}+ig$ superconductivity in Sr${}_2$RuO${}_4$
• Possibility of mixed helical p-wave pairings in Sr${}_2$RuO${}_4$
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr${}_2$RuO${}_4$ superconductor
• Fluctuation-driven superconductivity in Sr${}_2$RuO${}_4$ from weak repulsive interactions
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4
• Spin-orbit-assisted electron pairing in 1D waveguides
• Superconducting gap symmetry from Bogoliubov quasiparticle interference analysis on {Sr}${}_2${RuO}${}_4$
• Surface State of Inter-orbital Pairing State in Sr${}_2$RuO${}_4$ Superconductor
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Why Scanning Tunneling Microscopy on Sr${}_2$RuO${}_4$ sometimes doesn't see the superconducting gap