Van Hove singularities and nonadiabatic effects in superconductivity

The breakdown of Migdal's theorem implies the generalization of the electron-phonon theory of superconductivity to include various nonadiabatic effects. The reduced electronic screening due to the small carrier density and the presence of a van Hove singularity for the optimized cuprates complete a new scenario for both the superconductive and the normal state. In particular the van Hove singularity can be related to highest values of T-c, to the reduction of the isotope effect and to the linear resistivity.