Role of spin-orbit coupling on the spin triplet pairing in Na_{x}CoO_{2}yH_{2}O I: d-vector under zero magnetic field

TL;DR

This paper investigates how spin-orbit coupling influences the d-vector orientation in potential spin triplet superconductor Na_{x}CoO_{2}yH_{2}O, revealing different effects on p-wave and f-wave pairing states and aligning with experimental observations.

Contribution

It provides a microscopic analysis of the d-vector in spin triplet superconductivity considering spin-orbit coupling, highlighting the distinct effects on p-wave and f-wave states.

Findings

Spin-orbit coupling lifts degeneracy in pairing states.

d-vector aligns in-plane for p-wave pairing.

Degeneracy lifting is more significant in p-wave than in f-wave.

Abstract

The d-vector in possibile spin triplet superconductor Na_{x}CoO_{2}yH_{2}O is microscopically investigated on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. As a result of the perturbation theory, we obtain the stable spin triplet superconductivity where the p-wave and f-wave states can be stabilized. If we neglect the spin-orbit coupling, superconducting state has 6-fold (3-fold) degeneracy in the p-wave (f-wave) state. This degeneracy is lifted by the spin-orbit coupling. We determine the d-vector within the linearlized Dyson-Gorkov equation. It is shown that the d-vector is always along the plane when the pairing symmetry is p-wave, while it depends on the parameters in case of the f-wave state. The lifting of degeneracy is significant in the p-wave state while it is very small in the f-wave state. This is because the first order term with respect to the spin-orbit coupling is effective in the former case, while it is ineffective in the latter case. The consistency of these results with NMR and \muSR measurements are discussed.