Multi-orbital analysis on the Superconductivity in Na_{x}CoO_{2} \cdot y H_{2}O

TL;DR

This study constructs a three-orbital model for Na_{x}CoO_{2} ulyH_{2}O and finds that ferromagnetic spin fluctuations stabilize spin triplet superconductivity, with nearly degenerate p-wave and f-wave states influenced by orbital degeneracy.

Contribution

It introduces a comprehensive three-orbital model and analyzes the stability of various superconducting states, emphasizing the role of orbital degeneracy and ferromagnetic fluctuations.

Findings

Spin triplet superconductivity is stabilized over a wide parameter range.

Nearly degenerate p-wave and f-wave superconducting states are identified.

Vertex corrections induce screening but do not alter the qualitative results.

Abstract

We preform a multi-orbital analysis on the novel superconductivity in Na_{x}CoO_{2} \cdot yH_{2}O. We construct a three-orbital model which reproduces the band structure expected from the LDA calculation. The effective interaction leading to the pairing is estimated by means of the perturbation theory. It is shown that the spin triplet superconductivity is stabilized in the wide parameter region. This is basically owing to the ferromagnetic character of spin fluctuation. The p-wave and f-wave superconductivity are nearly degenerate. The former is realized when the Hund's rule coupling is large, and vice versa. In a part of the parameter space, the d-wave superconductivity is also stabilized. We point out that the orbital degeneracy plays an essential role for these results through the wave function of quasi-particles. The nearly degeneracy of p-wave and f-wave superconductivity is explained by analysing the orbital character of each Fermi surface. We discuss the validity of some reduced models. While the single band Hubbard model reproducing the Fermi surface is qualitatively inappropriate, we find an effective two-orbital model appropriate for studying the superconductivity. We investigate the vertex corrections higher than the third order on the basis of the two-orbital model. It is shown that the vertex correction induces the screening effect but does not affect on the qualitative results.