Spin-triplet superconductivity in Sr2 RuO4 due to orbital and spin fluctuations: Analyses by two-dimensional renormalization group theory and self-consistent vertex-correction method

We study the mechanism of the triplet superconductivity (TSC) in Sr2RuO4 based on the multiorbital Hubbard model. The electronic states are studied using the recently developed renormalization group method combined with the constrained random-phase approximation, called the RG + cRPA method. Thanks to the vertex correction (VC) for the susceptibility, which is dropped in the mean-field-level approximations, strong orbital and spin fluctuations at Q≈(2π/3,2π/3) emerge in the quasi-one-dimensional Fermi surfaces (FSs) composed of dxz+dyz orbitals. Due to the cooperation of both fluctuations, we obtain the triplet superconductivity in the Eu representation, in which the superconducting gap is given by the linear combination of (Δx(k),Δy(k))∼(sin3kx,sin3ky). Very similar results are obtained by applying the diagrammatic calculation called the self-consistent VC method. Thus, the idea of "orbital + spin fluctuation mediated TSC" is confirmed by both the RG + cRPA method and the self-consistent VC method. We also revealed that the large superconducting gap on the dxy-orbital Fermi surface is induced from gaps on the quasi-one-dimensional FSs, in consequence of the large orbital mixture due to the 4d spin-orbit interaction.