From charge fluctuations to pairing instabilities: Nonperturbative enhancement of the electron-phonon coupling driven by electronic correlations

We present a dynamical mean-field theory (DMFT) study of the nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in strongly correlated electron systems. Using DMFT for the single band Hubbard model on the square lattice, we analyze corrections to second-order electron-phonon processes arising from electronic fluctuations near the Mott metal-to-insulator transition (MIT). In this regime, the isothermal charge response becomes particularly large at small momenta, signaling the tendency toward phase-separation instabilities and enabling a substantial enhancement of the effective electron-phonon coupling. Finally, we critically discuss the impact of our findings on observable spectral quantities as well as possible implications for the emergence of pairing instabilities.