Anisotropic superconductivity in the 2D Hubbard model: Gap function and interaction weight

A potential ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ pairing state in the 2D Hubbard model is investigated within a conserving extension of Hartree-Fock theory known as the fluctuation exchange approximation. The self-consistent field equations are solved with the aid of a recently developed renormalization group approach for general models which lack a Migdal theorem. The calculations yield an anisotropic gap which saturates rapidly below ${\mathit{T}}_{\mathit{c}}$ to a peak value of 2${\mathrm{\Delta }}_{\mathbf{k}}$/${\mathit{kT}}_{\mathit{c}}$∼10–12 for k along the ${\mathit{k}}_{\mathit{x}}$ and ${\mathit{k}}_{\mathit{y}}$ axes.