A survey of nonadiabatic superconductivity in cuprates and fullerides

High-T-c superconductors are characterized by very low carrier densities. T his feature leads to two fundamental consequences: on one hand the Fermi en ergies are correspondingly smalt and they can be of the same order of phono n frequencies. In such a situation nonadiabatic corrections arising from th e breakdown of Migdal's theorem can not be longer neglected. In addition, s mall carrier densities imply poor screening and correlation effects have to be taken into account. We present a comprehensive overview of the theory o f superconductivity generalized into the nonadiabatic regime which is quali tatively different from the conventional one. In this framework some of the observed properties of the cuprates and the fullerene compounds can be nat urally accounted for, and a number of theoretical predictions are proposed that can be experimentally tested.