The Electron-Phonon Interaction in the Presence of Strong Correlations

TL;DR

This paper explores how strong electron-electron interactions modify electron-phonon coupling, revealing conditions that suppress or enhance interactions and potentially lead to phase separation or superconductivity in correlated materials.

Contribution

It provides a detailed analysis of electron-phonon interactions under strong correlations, including vertex corrections and their impact on phase stability and pairing mechanisms.

Findings

Vertex corrections suppress effective electron-phonon coupling at high momentum transfer.

Strong correlations can induce phase separation instability.

Phonon exchange may lead to superconducting instabilities near phase separation.

Abstract

We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view: the strong interaction is responsible for vertex corrections, which are strongly dependent on the $v_Fq/\omega$ ratio. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the $v_Fq/\omega \gg 1$ limit. However, such effect is not present when $v_Fq/\omega \ll 1$. Analyzing the Landau stability criterion, we show that a sizable electron-phonon interaction can push the system towards a phase-separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.