Superconductivity of the Two-Dimensional Hubbard Model with a Small U

Abstract

Superconductivity of the two-dimensional Hubbard model with t^′=0 has been examined in the small U limit, where the matrix element of pair scattering is expressed as V_kk^′=U+U²χ (k+k^′). The susceptibility χ (k) of the unperturbed band has been evaluated accurately and the gap equation, which reduces to a seqular equation, has been solved precisely. The gap is found to be of the form ∝exp (-2t²/xU²), where x is the eigenvalue of the seqular equation. We have found the largest eigenvalue x is always positive (superconductive). The symmetry of the gap function is b_1g for the electron density n_e>0.6 and b_2g for n_e<0.6, depending on the peak position of χ (k). It is roughly (π , π ) for the former case and (π, 0) for the latter. The superconductivity seems to prevail even for n_e→ 0. These results can be explained with a simple criterion.