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 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 (Δ_x(k),Δ_y(k))∼(sin3k_x,sin3k_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.

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