Role of spin-orbit interaction on the superconductivity in Na_x CoO₂ · y H₂ O: Phase diagram under the magnetic field

The d-vector in possible spin triplet superconductor Na_x CoO₂ · y H₂ O is microscopically analyzed on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. As a result of the perturbation theory, it is shown that the d-vector is parallel to the plane when the pairing symmetry is p-wave, while both over(d, ^) ∥ xy and over(d, ^) ∥ z are possible in the f-wave state. We point out that the multiple phase transitions are expected under the in-plane magnetic field when the pairing symmetry is p-wave.