Electron-phonon interaction in proximity of a Mott transition

The effects of electron-phonon interaction on the electronic properties of a strongly correlated metal on the verge of a Mott metal-insulator transition are studied by means of dynamical mean-field theory. We show that electron-phonon interactions induce a phase separation instability close to the density driven Mott transition, and give rise to significant renormalization of electronic properties like charge susceptibility. Nonetheless, the strong correlation reduces the effectiveness of the electron-phonon coupling in driving a polaronic crossover.