  We study the hole binding energy and pairing correlations in the three-band
Hubbard model coupled to an apical oxygen phonon, by exact diagonalization and
constrained-path Monte Carlo simulations. In the physically relevant
charge-transfer regime, we find that the hole binding energy is strongly
enhanced by the electron-phonon interaction, which is due to a novel
potential-energy-driven pairing mechanism involving reduction of both
electronic potential energy and phonon related energy. The enhancement of hole
binding energy, in combination with a phonon-induced increase of quasiparticle
weight, leads to a dramatic enhancement of the long-range part of d-wave
pairing correlations. Our results indicate that the apical oxygen phonon plays
a significant role in the superconductivity of high-$T_c$ cuprates.
