Second-neighbor hopping in the attractive Hubbard model

We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (${\mathit{t}}_2$) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large ‖U‖, ${\mathit{t}}_2$ induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with ${\mathit{t}}_2$.