Solution for the<i>U</i>-negative Hubbard superconductor including second-order correlation effects

We analyze the effects of fluctuations on the gap and critical temperature of a superconductor. The model Hamiltonian chosen is one of the simplest: the U-negative Hubbard model. A diagrammatic self-consistent approach is used, and a second-order self-energy is calculated in order to take into account local fluctuations. Our results show a decrease of the superconductor gap and critical temperature with respect to the mean-field solution. The ratio 2\ensuremath{\Delta}/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$ is not modified, however, by the local fluctuations if the self-energy matrix in a site representation extends only to the lattice nearest neighbors. In this approximation, the superconductor gap is found to be constant along the Fermi surface. Further nearest-neighbor interactions introduce a superconductor gap that changes along this surface.

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