Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons

TL;DR

This paper explores how strongly correlated electrons interact with phonons via polarons, suggesting that phonon cloud exchange can lead to polaron pairing and potentially superconductivity, with the collective mode frequency influencing the transition temperature.

Contribution

It introduces a model where polarons exchanging phonon clouds induce pairing, highlighting the role of collective phonon modes in superconductivity within the Hubbard-Holstein framework.

Findings

Polaron exchange of phonon clouds can lead to pairing.

Superconductivity may be driven by collective phonon mode frequencies.

On-site Coulomb repulsion can be exactly canceled by phonon-mediated attraction.

Abstract

We investigate the interaction of strongly correlated electrons with phonons in the frame of the Hubbard-Holstein model. The electron-phonon interaction is considered to be strong and is an important parameter of the model besides the Coulomb repulsion of electrons and band filling. This interaction with the nondispersive optical phonons has been transformed to the problem of mobile polarons by using the canonical transformation of Lang and Firsov. We discuss in particular the case for which the on-site Coulomb repulsion is exactly cancelled by the phonon-mediated attractive interaction and suggest that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. It is then the frequency of the collective mode of phonon clouds being larger than the bare frequency, which determines the superconducting transition temperature.