Crossover between BCS superconductor and BEC states in the attractive Anderson lattice model

Abstract

Using the method of Green functions equation of motion we considered the three dimensional Anderson lattice model with attractive interaction between f-electrons. We studied the appearance of superconductivity as a function of this attractive interaction and a hybridization between localized f-electrons and conduction c-electrons. The zero temperature phase diagram as a function of the hybridization and the strength of the attractive interaction is obtained. In this phase diagram a quantum phase transition is found which is characterized by a break up of the conventional BCS superconductor state, as the hybridization increases after a certain critical value, Vc, and, at the same time, the beginning of a metallic-like state with preformed pairs. At sufficiently large attractive interactions and for V>Vc, a superfluid state of Bose condensed pairs appears. We investigate for a possible coexistence between these pairs that form the superfluid state, characterized by gapped dispersion relations, and the metallic-like state characterized by gapless electronic excitations.