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

TL;DR

This study uses the functional renormalization group method to analyze how vertex corrections enhance charge-orbital fluctuation-mediated superconductivity in multiorbital systems, especially Fe-based superconductors.

Contribution

It demonstrates that electron-boson vertex corrections significantly amplify charge/orbital fluctuation pairing interactions in multiorbital models.

Findings

Charge-channel electron-boson coupling is greatly enhanced by vertex corrections.

Orbital fluctuation pairing mechanism is viable due to increased effective interactions.

Spin fluctuation pairing is suppressed by vertex corrections.

Abstract

In various multiorbital systems, the emergence of the orbital fluctuations and its role on the pairing mechanism attract increasing attention. To archive deep understanding on these issues, we perform the 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.