Suppression of superconductivity in the Hubbard model by buckling and   breathing phonons
  We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects, an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppress superconductivity. Due to the later effect we find that buckling and breathing phonons suppress the superconductivity in the region of parameter space relevant for cuprate superconductors. 
Alexandru Macridin, Brian Moritz, Mark Jarrell, Thomas Maier