Spin-triplet superconductivity in Sr2RuO4 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 approximate to (2 pi/3,2 pi/3) emerge in the quasi-one-dimensional Fermi surfaces (FSs) composed of d(xz) + d(yz) orbitals. Due to the cooperation of both fluctuations, we obtain the triplet superconductivity in the E-u representation, in which the superconducting gap is given by the linear combination of (Delta(x)(k), Delta y(k)) similar to (sin 3k(x), sin 3k(y)). 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 d(xy)-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.