d-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interactio n leads to a strong momentum dependance in the generalized Eliashberg equat ions beyond Migdal's limit. For a s-wave symmetry of the order parameter, t his induced momentum dependence leads to an enhancement of T-c when small m omentum transfer is dominant. Here we study how the d-wave symmetry affects the above behavior. We find that the nonadiabatic corrections depend only weakly on the symmetry of the order parameter provided that only small mome ntum scatterings are allowed for the electron-phonon interaction. In this s ituation, We show that also for a d-wave symmetry of the order parameter, t he nonadiabatic corrections enhance T-c. We also discuss the possible inter play and crossover between s- and d-wave depending on the material's parame ters.