Superconducting critical temperature, for s-wave symmetry order parameter, for intermediate correlated electron systems

Abstract

We calculate the superconducting critical temperature, T c, for an s-wave order parameter, in the presence of local Coulomb interactions by using a normal state one particle Green function, G N ( k → , iω n) , which is renormalized by the interactions. In the end, we adopt for G N ( k → , iω n) a Hubbard-III like approximation since it can give a normal metal–insulator transition and as such can be used to study T c vs. U for intermediate values of U, going beyond the mean-field treatment for the local Coulomb interaction, U. However, the equation for T c is mean-field like with respect to the pairing interaction, V, which we assume with a different origin than the repulsive part. We have calculated: (1) T c vs. U for different values of V and chemical potential, μ; (2) T c vs. ρ≡ n/2 for different values of V and U. The conclusions we reach are: (a) the local Coulomb interaction is always detrimental to superconductivity, namely, T c goes down with increasing U; (b) the maximum value of T c is reached away from half-filling, contrary to the pure BCS-case ( U≡0). Results (a) have also been obtained in non-Fermi liquid theories. We have compared our results with known relevant work.