Ch. Pao et Hb. Schuttler, SUPERCONDUCTING INSTABILITY IN THE HOLSTEIN-HUBBARD MODEL - A NUMERICAL RENORMALIZATION-GROUP STUDY, Physical review. B, Condensed matter, 57(9), 1998, pp. 5051-5054
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.