Superconductivity in a narrow-band system with intersite electron pairing in two dimensions: A mean-field study

We study a simple model for superconductivity based on the extended Hubbard model with on-site repulsive and intersite attractive interactions for arbitrary electron density using the mean-field approach. We perform detailed numerical studies of anisotropic superconductivity of $s$, $p$, and $d$ type for the two-dimensional square lattice with nearest- and next-nearest-neighbor hopping. For a nearly half-filled band the $d$-wave pairing is most stable. $p$-wave and then extended $s$-wave pairings become stable upon decreasing the band filling. While $T_c$ for $d$- and $p$-wave pairings smoothly decrease with band filling, $s$-wave pairing shows strong nonmonotonic behavior of $T_c$ versus electron density. Inclusion of next-nearest-neighbor hopping changes essentially the behavior of $T_c$ and the mutual stability of anisotropic pairings. The competition between superconductivity and the spin-density-wave state is studied. The question of the transition from Cooper pairs to intersite pairs and their Bose condensation is discussed. We also consider the limit of strong correlations and its connection with recent theoretical proposals for the superconductivity in high-$T_c$ oxides. Our findings are discussed in connection with the experimental studies of superconductivity and magnetism in ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$-based compounds.