Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value VC for the attractive interaction is required to obtain a superconducting state. For finite temperature T < TC a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap Δ and TC depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio 2Δ(0)/TC varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n.