Some properties of two-band superconductors: Role of k-dependent hybridization

Abstract

We discuss the influence of a k-dependent hybridization on a superconducting material described by a two-band model, within an extended BCS picture. The effect of hybridization is to create in the normal state new bands with mixed features and the k-dependence arises from its non-local character. We consider a broad s-p conduction band hybridized with a narrow d-band, assuming that the pairing occurs at the d-band ( singlet d-d pairing). We calculate self-consistently the BCS type order parameter Δ and the critical temperature T c . We verify that T c is stable when hybridization is turned on until a critical value of V = V c and both the “phononic” and electronic parts of T c are renormalized by a parameter α, which gives the ratio of the effective band masses. We calculate the value of 2 Δ(0)/ k B T c and compare with standard BCS results. The isotope effect is almost the same in the whole range of 0 ≤ V < V c energy.