Superconducting correlations in the two-dimensional Hubbard model with long-range electron hopping

Projector quantum Monte Carlo calculations are used to examine superconducting correlations in the two-dimensional Hubbard model with exponentially decaying electron hopping amplitudes tij(q) similar to  q|Ri Rj|. It is shown that this type of hopping, which models more realistically (in comparison to the nearest-neighbor hop-ping) the situation in real transition-metal materials, stabilizes significantly the superconducting correlations in the d-wave channel for electron concentrations n above the quarter band filling, especially for q similar to 0.35. In this region the enhancement of the superconducting correlations at non-zero q, against the classical Hubbard limit (q = 0), changes (depending on the electron concentration) from 2 in the worse case to 5 in the best case. Moreover, we have studied also the influence of the Coulomb interaction U and a disorder on superconducting correlations. We have found that the Coulomb interaction enhances significantly superconducting correlations in the d-wave channel, while a disorder suppresses them gradually, but they surprisingly persist up to the disorder strength comparable to the Coulomb interaction.