In various multiorbital systems, the emergence of the orbital fluctuations and their role on the pairing mechanism attract increasing attention. To achieve deep understanding on these issues, we perform a functional renormalization group (fRG) study for the two-orbital Hubbard model. The vertex corrections for the electron-boson coupling (U-VC), which are dropped in the Migdal-Eliashberg gap equation, are obtained by solving the RG equation. We reveal that the dressed electron-boson coupling for the charge channel Uˆ^c_eff becomes much larger than the bare Coulomb interaction Uˆ⁰ due to the U-VC in the presence of moderate spin fluctuations. For this reason, the attractive pairing interaction due to the charge or orbital fluctuations is enlarged by the factor (Uˆ^c_eff/Uˆ⁰)²≫1. In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel U-VC, because of the relation Uˆ^s_eff≪Uˆ⁰. The present study demonstrates that the orbital or charge fluctuation pairing mechanism can be realized in various multiorbital systems thanks to the U-VC, such as in Fe-based superconductors.

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