Spin gap and superconductivity in the three-dimensional attractive Hubbard model

Abstract

We study the phase diagram for the attractive (i.e., negative-U) Hubbard model on a simple-cubic lattice, through Monte Carlo simulations. We obtain the critical temperature ${\mathit{T}}_{\mathit{c}}$ for superconductivity from a finite-size scaling analysis of the data for the pairing correlations. For fixed on-site attraction U, ${\mathit{T}}_{\mathit{c}}$ displays a maximum near the filling factor 0.9, roughly independent of U. For fixed filling we estimate the crossover temperature ${\mathit{T}}^{\ifmmode\times\else\texttimes\fi{}}$(U), separating the normal states: metallic and spin gap. There is also a critical value ${\mathit{U}}_{\mathit{p}}$ for pair formation, the magnitude of which seems to be independent of doping. The relevance of these results to the high-${\mathit{T}}_{\mathit{c}}$ oxides is discussed.