Functional renormalization group study of orbital fluctuation mediated superconductivity: Impact of the electron-boson coupling vertex corrections

摘要

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 U_(eff)~c becomes much larger than the bare Coulomb interaction U~0 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 (U_(eff)~c/U~0)~2 (＞＞) 1. In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel U-VC, because of the relation U_(eff)~s (＜＜) U~0. 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.