Possible phononic mechanism for d(x(2)-y(2)) superconductivity in the presence of short-range antiferromagnetic correlations

We discuss the high-temperature superconductors in a regime where the antiferromagnetic (AF) correlation length is only a couple of lattice spacings. In the model proposed here, these short-range AF fluctuations play an essential role in the dressing of the carriers, but the attraction needed for superconductivity arises from a transverse phonon oxygen mode with a finite buckling angle as it appears in YBa2Cu3O7-delta. A Simple fermion-phonon model analog to the Holstein model is introduced to account for this effect. We argue that the model has a d(x2-y2)-wave superconducting ground state. The critical temperature (T-c) and the O-isotope effect coefficient (alpha(0)) versus hole density (x) are in qualitative agreement with experiments for the cuprates. The minimum (maximum) of alpha(0) (T-c) at optimal doping is caused by a large peak in the density of states of holes dressed by AF fluctuations, as discussed in previous van Hove scenarios.