Superconductivity of the Two-Dimensional Hubbard Model with a Small U : Condensed Matter: Electronic Properties, etc.

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Superconductivity of the two-dimensional Hubbard model with t' = O has been examined in the small U limit, where the matrix element of pair scattering is expressed as V_<kk'>, = U+U^2_X(k+k') . The susceptibility _X(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(-2t^2/xU^2), 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 _X(k). It is roughly (π, π) for the former case and (π, O) for the latter. The superconductivity seems to prevail even for n_e ⇾ 0. These results can be explained with a simple criterion.
社団法人日本物理学会の論文
2001-03-15