# Plain $s$-wave superconductivity near the magnetic criticality: Enhancement of attractive electron-boson coupling vertex corrections

## TL;DR

This paper explains the emergence of plain s-wave superconductivity near magnetic criticality through vertex corrections that enhance electron-phonon interactions and orbital fluctuations, despite strong Coulomb repulsion.

## Contribution

It demonstrates how higher-order vertex corrections significantly amplify phonon-mediated interactions, leading to s-wave pairing near magnetic criticality in multiorbital systems.

## Key findings

- Vertex corrections enhance orbital fluctuations and electron-phonon coupling.
- Plain s-wave state arises despite Coulomb repulsion near magnetic criticality.
- Multiorbital screening reduces Coulomb repulsion for Cooper pairs.

## Abstract

Recent experiments revealed that the plain $s$-wave state without any sign-reversal emerges in various metals near the magnetic criticality. To understand this counter-intuitive phenomenon, we study the gap equation for the multiorbital Hubbard-Holstein model, by analyzing the vertex correction (VC) due to the higher-order electron-correlation effects. We find that the phonon-mediated orbital fluctuations are magnified by the VC for the susceptibility ($\chi$-VC). In addition, the charge-channel attractive interaction is enlarged by the VC for the coupling-constant ($U$-VC), which is significant when the interaction has prominent $q$-dependences so the Migdal theorem fails. Due to both $\chi$-VC and $U$-VC, the plain $s$-wave state is caused by the small electron-phonon interaction near the magnetic criticality against the repulsive Coulomb interaction. We find that the direct Coulomb repulsion for the plain $s$-wave Cooper pair is strongly reduced by the "multiorbital screening effect".