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

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) 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 scale Tco where the renormalization group flow crosses over from the regime (Λ > Tco) where the electron-electron (e-e) and electron-hole (eh) 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. After diagonalization of VΛ=Tco , we identify its most attractive eigenvalue λmin. 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. Using the form of pairing and the structure of the renormalization group equations in the low energy regime, we give our interpretation of ARPES experiments trying to determine the symmetry of the order parameter in the Bi2212 high-Tc compound.