Superconductivity from long-range interaction: A crossover between the electron gas and the lattice model

We explore how the superconductivity arising from the on-site electron-electron repulsion changes when the repulsion is made long-ranged, 1∕r-like interaction by introducing an extended Hubbard model with the repulsion extended to distant (12th) neighbors. With a simplified fluctuation-exchange approximation, we have found for the square lattice that: (i) As the band filling becomes dilute enough, the charge susceptibility becomes comparable with the spin susceptibility, where p- and then s-wave pairings become relatively dominant, in agreement with the result for the electron gas by Takada, while (ii) the d wave, which reflects the lattice structure, dominates well away from the half-filling. All of these can be understood in terms of the spin and charge structures along with the shape and size of the Fermi surface.