Tail-like regime and BCS-BEC crossover due to hybridization in a two-band superconductor

Superconductivity in strongly correlated systems is a remarkable phenomenon that attracts huge interest. The study of this problem is relevant for materials such as the high T _c oxides, pnictides and heavy fermions. These systems also have in common the existence of electrons of several orbitals that coexist at a common Fermi surface. In this paper we study the effect of pressure, chemical or applied on multi-band superconductivity. Pressure varies the atomic distances and consequently the overlap of the wave-functions in the crystal. This rearranges the electronic structure that we model including a pressure dependent hybridization between the bands. We consider the case of two-dimensional systems in a square lattice with inverted bands. We study the conditions for obtaining a pressure induced superconductor quantum critical point and show that hybridization, i.e. pressure can induce a Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover in multi-band systems even for moderate interactions. We found a tail-like superconductor regime and briefly discuss the influence of the symmetry of the order parameter in the results.