Self-consistent weak-coupling study of the three-bandCuO2model

The ‘‘fluctuation-exchange’’ approximation, a Baym-Kadanoff theory used previously to treat the one-band Hubbard model, is used to investigate a three-band model for the ${\mathrm{CuO}}_2$ planes in the cuprate superconductors. Attention is restricted to (a) nearest-neighbor copper-oxygen hopping and (b) a Hubbard-like Coulomb interaction on copper sites only. Orbital-occupancy factors are shown to be in good agreement with previous quantum simulation studies. An instability eigenvalue analysis confirms that, as in the one-band model, the most likely channel for superconductivity is a ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ singlet. The scale for onset of exponentially long-ranged antiferromagnetic correlations is compared with results for the one-band model, and the role of hybridization in reducing the effective Coulomb interaction is studied using a transformation to Wannier states.