Self-consistent ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ pairing in a two-dimensional Hubbard model

Results of a conserving fluctuation exchange calculation for the superconducting state of a two-dimensional Hubbard model are presented. Self-consistent solutions for the full momentum- and frequency-dependent gap, renormalization, and frequency shift parameters have been obtained. The resulting frequency- and momentum-dependent gap is found to have ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ symmetry. Below ${\mathit{T}}_{\mathit{c}}$, the maximum gap opens rapidly to a low temperature 2Δ(0)/${\mathit{kT}}_{\mathit{c}}$ value of order 10. We find that the effective interaction arising from the exchange of spin and charge fluctuations is stabilized by self-energy feedback effects as the superconducting gap opens.