Nonadiabatic theory of the superconducting state

Fermi energies in fullerene compounds and cuprates are extremely small as c onsequence of the small number of charge carriers and are comparable to the phonon frequency scale. In this situation the conventional Migdal-Eliashbe rg theory does not hold anymore and nonadiabatic effects need to be taken i nto account. In previous studies, a generalization of Eliashberg theory in the nonadiabatic regime has been proposed to calculate normal state propert ies and the onset temperature T-c of the superconductive phase. Here we ext end the nonadiabatic theory below T-c where the opening of the superconduct ing order parameter affects the nonadiabatic correction. The superconductin g gap Delta is calculated in a self-consistent way. We find that large valu es of the ratio 2 Delta /T-c are obtained in the nonadiabatic theory by sma ller electron-phonon coupling lambda than in Migdal-Eliashberg theory. This agrees with the picture that strong-coupling phenomenology can be achieved in nonadiabatic theory by "reasonable" values of lambda. We apply our anal ysis to the case of the fullerene compounds.