Electron-Phonon Interactions in the W=0 Pairing Scenario

TL;DR

This paper explores how phonons and electron correlations interact to influence superconducting pairing in cuprates, using a model that combines Hubbard interactions with electron-phonon couplings, revealing complex behaviors at different coupling strengths.

Contribution

It introduces a combined model of electron-electron and electron-phonon interactions to analyze W=0 pairing, providing analytical and numerical insights into their interplay in cuprate-like systems.

Findings

Half-breathing phonon modes enhance pairing at weak coupling.

The model exhibits complex behavior at intermediate and strong coupling.

W=0 pairing mechanism persists under certain symmetry conditions.

Abstract

We investigate the interplay of phonons and correlations in superconducting pairing by introducing a model Hamiltonian with on-site repulsion and couplings to several vibration branches having the Cu-O plane of the cuprates as a paradigm. We express the electron-phonon coupling (EP) through two force constants for O-Cu and O-O bond stretchings. Without phonons, this reduces to the Hubbard Model, and allows purely electronic W=0 pairing. A W=0 pair is a two-body singlet eigenstate of the Hubbard Hamiltonian, with no double occupancy, which gets bound from interactions with background particles. Indeed, this mechanism produces a Kohn-Luttinger-like pairing from the Hubbard repulsion, provided that its symmetry is not severely distorted. From the many-body theory, a canonical transformation extracts the effective two-body problem, which lends itself to numerical analysis in case studies. As a test, we use as a prototype system the $\cu$ cluster. We show analytically that at weak EP coupling the additive contributions of the half-breathing modes reinforce the electronic pairing. At intermediate and strong EP coupling and $U \sim t$, the model behaves in a complex and intriguing way.