Binding of holes in the Hubbard model with next-nearest-neighbor hopping

We study the two-dimensional Hubbard model with next-nearest-neighbor hoppings and its related strong-coupling effective Hamiltonian by exact diagonalization. We found that the binding energy of holes tends to be smaller than with nearest neighbors only. However, the tendency towards phase separation is reduced by increasing the next-nearest-neighbor hopping. By studying pairing correlations, we found that the mode is strongly enhanced when the second-neighbor interactions are turned on.