Superconducting instabilities of the non-half-filled Hubbard model in two dimensions

Abstract

The problem of weakly correlated electrons on a square lattice is formulated in terms of a one-loop renormalization group. Starting from the action for the entire Brillouin zone we reduce successively the cutoff Λ about the Fermi surface and follow the renormalization of the coupling U as a function of three energy-momenta. We calculate the intrinsic temperature scale Tco where the renormalization-group flow crosses over from the regime (Λ>Tco) where the electron-electron (e-e) and electron-hole (e-h) terms are equally important to the regime (Λ<Tco) where only the e-e term plays a role. In the low-energy regime only the pairing interaction V is marginally relevant, containing contributions from all renormalization-group steps of the regime Λ>Tco. We identify the most attractive eigenvalue λmin of VΛ=Tco. At low filling, λmin corresponds to the B2 representation (dxy symmetry), while near half filling the strongest attraction occurs in the B1 representation (dx2−y2 symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. We also give a possible interpretation of angle-resolved photoemission spectroscopy experiments trying to determine the symmetry of the order parameter in the high-Tc compound Bi2Sr2CaCu2O8. © 1996 The American Physical Society.

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