Superconductivity in a narrow-band system with intersite electron pairing in two dimensions. II. Effects of nearest-neighbor exchange and correlated hopping

Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange ($J$) and correlated hopping ($K$) interaction. Detailed numerical analysis of $s$-, $p$-, and $d$-wave pairing solutions is performed for the two-dimensional square lattice with nearest- ($t$) and next-nearest- ($t_2$) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the $d$-wave and the extended $s$-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the $\frac{t_2}{t}$ ratio, giving in particular for $t_2=0\mathrm{}$ $s$-wave ($d$-wave) pairing as most favorable in the low (high) density limit, but increasing $t_2$ can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects $s$-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.