Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm. We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space. The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory. The self-consistent equation for the pair potential is derived and solved. Somewhat contrary to expectation, a weak attractive U comparable to the pair potential can destroy the superconductivity, whereas for weak to intermediate repulsive U , the pair potential can be enhanced. The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation. We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors, in contrast to the uncorrelated BCS limit.
We investigate the possibility of superconductivity and estimate the transition temperature
Tc in a system in which the bare electron-electron interaction
V(q) is arbitrary but basically repulsive. We employ the recently developed variational method which is believed to be the best one for the purpose at present. Through this study, we consider a concept of the Cooper pair originating not from an attractive but rather a repulsive bare potential. We find a special form for
V(q) to obtain
Tc over 200 K in the dilute electron-gas system. We discuss the band structure near the Fermi surface to produce such
V(q)′s and propose a new exciton mechanism.