Possibility of f-wave spin-triplet superconductivity in the CoO2 superconductor:: A case study on a 2D triangular lattice in the repulsive Hubbard model

Stimulated by the recent finding of the superconductivity in Na0.35CoO2.1.3H(2)O, we investigate superconducting instabilities on a 2D triangular lattice in the repulsive Hubbard model. Using the third-order perturbation expansion with respect to the on-site repulsion U, we evaluate the linearized Dyson-Gor'kov equation. We find that f-wave spin-triplet pairing is the most stable in a wide range of the next-nearest-neighbor hopping integral t' and electron number density n. The introduction of t' is crucial for adjusting the van Hove singularities to the neighborhood of the Fermi surface crossing around the K point. In this case, the bare spin susceptibility shows a broad peak around the Gamma point. These conditions stabilize f-wave pairing. Although f-wave pairing is also given by the fluctuation-exchange approximation, the transition temperature is too low to be observed. This is because the depairing effect by the spin fluctuation is overestimated. Thus, the third-order vertex corrections are important for the spin-triplet superconductivity, similar to the case of Sr2RuO4.