Electron-phonon interaction in the t-J model

TL;DR

This paper derives a t-J model incorporating electron-phonon interactions from a three-band model, explaining phonon softening phenomena observed experimentally in doped materials.

Contribution

It introduces a comprehensive t-J model with electron-phonon coupling considering both hopping and Coulomb integral modulations, highlighting the dominant role of hopping modulation.

Findings

Explains anomalous softening of half-breathing phonon mode upon doping.

Shows weaker softening of breathing mode and negligible coupling to buckling modes.

Identifies modulation of hopping integrals as the primary electron-phonon interaction mechanism.

Abstract

We derive a t-J model with electron-phonon coupling from the three-band model, considering modulation of both hopping and Coulomb integrals by phonons. While the modulation of the hopping integrals dominates, the modulation of the Coulomb integrals cannot be neglected. The model explains the experimentally observed anomalous softening of the half-breathing mode upon doping and a weaker softening of the breathing mode. It is shown that other phonons are not strongly influenced, and, in particular, the coupling to a buckling mode is not strong in this model.