SUPERCONDUCTING INSTABILITY IN THE HOLSTEIN-HUBBARD MODEL - A NUMERICAL RENORMALIZATION-GROUP STUDY

We have studied the d-wave pairing instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation-exchange app roximation which treats both Coulomb and electron-phonon (EP) interact ion diagrammatically on an equal footing. A generalized numerical reno rmalization-group technique has been developed to solve the resulting self-consistent field equations. The d-wave superconducting phase diag ram shows an optimal T-c at electron concentration [n]similar to 0.9 f or the purely electronic Hubbard system. The EP interaction suppresses the d-wave T-c which drops to zero when the phonon-mediated on-site a ttraction U-p becomes comparable to the on-site Coulomb repulsion U. T he isotope exponent alpha is negative in this model and small compared to the classical BCS value alpha(BCS)=1/2 or compared to typical obse rved values in nonoptimally doped cuprate superconductors.