d-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependance in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced momentum dependence leads to an enhancement of T-c when small momentum 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 momentum scatterings are allowed for the electron-phonon interaction. In this situation, We show that also for a d-wave symmetry of the order parameter, the nonadiabatic corrections enhance T-c. We also discuss the possible interplay and crossover between s- and d-wave depending on the material's parameters.