Collective modes and superconductivity in an extended Hubbard model for copper oxide superconductors

A three-band extended Hubbard model for ${\mathrm{CuO}}_2$ planes is explored within a self-consistent-field approximation. The collective modes for both charge and spin fluctuations are calculated, including leading-order self-energy corrections for the quasiparticle propagators; this leads to an approximate form for the renormalized quasiparticle interactions, used to study superconductive pairing. We find that spin fluctuations promote pairing of ${\mathit{B}}_{1\mathit{g}}$ symmetry (${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$), and charge fluctuations between Cu and O induce either ${\mathit{A}}_{1\mathit{g}}$ (extended s) or ${\mathit{B}}_{2\mathit{g}}$ (${\mathit{d}}_{\mathit{x}\mathit{y}}$) pairing.