The role of local repulsive interactions on superconductor quantum critical points

► In the BEC limit a spread of values of the SC gap is induced by a weak repulsion. ► The Hubbard-I approach was used to treat the strong repulsions case. ► Strong repulsions renormalize the narrow band by a band-filling term. ► The T = 0 phase diagrams shows the attractive interactions as hybridization function. ► The two-band model with a renormalized narrow band is enough to describe the SCES.