Pairing, condensation, and superconductivity described by a Hubbard model with an attractive interaction

Abstract

We have developed a method for studying superconductivity in the negative-U Hubbard model. It is based on the Hubbard-alloy-analogy approximation applied to the Gor'kov equation for the model. We find that, unlike the case of the BCS solution, the formation of pairs and their condensation into a superconducting ground state take place at two different temperatures. We calculate the condensation temperature ${\mathit{T}}_{\mathit{c}}$ for all U and discuss the nature of the normal state which, for large enough U, features a macroscopically large number of pairs. Briefly, we argue that the model has relevance for high-temperature superconductors.