Role of spin-orbit coupling on the spin triplet pairing in Na_{x}CoO_{2}yH_{2}O II: Multiple phase diagram under the magnetic field

TL;DR

This paper investigates how spin-orbit coupling influences the multiple superconducting phases in Na_{x}CoO_{2}yH_{2}O, revealing stable spin triplet states and complex phase diagrams under magnetic fields.

Contribution

It introduces a detailed analysis of the multiple superconducting phases considering spin-orbit coupling and magnetic effects, highlighting the coexistence of p- and f-wave states.

Findings

Stable spin triplet pairing states are identified.

The p+f coexistence phase appears at low temperatures.

Distinct phase diagrams are shown for different pairing symmetries.

Abstract

The possibility of multiple phase diagram in the novel superconductor Na_{x}CoO_{2}yH_{2}O is analyzed on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. We have shown that the spin triplet pairing state is stable in this model. The p-wave (f-wave) state is stabilized when the Hund's rule coupling is large (small). In the precedent paper, we have determined the direction of d-vector at T=Tc and H=0 within the linearized Dyson-Gorkov equation. In this paper, the pairing state below Tc and under the magnetic field is determined within the weak coupling approximation including the paramagnetic effect. We find that the p+f coexistent state is stabilized at low temperatures in a part of parameter range. We point out that the phase diagram in the H-T plane is quite different between the p-wave, f-wave and p+f-wave superconductivities. The characteristics of each phase are clarified by showing the magnetic susceptibility and specific heat. We discuss the comparison with experimental results and suggest some future experiments to detect the multiple phase transition.