An Alternative Route to D-wave Superconductivity: the Charge Channel

We demonstrate that a $d_{x^2-y^2}$ superconducting pairing is naturally associated with the screened Coulomb interaction $V_{eff}({\bf q},\omega)$ within the $CuO_2$ plane of high $T_c$ superconductors. This pairing instability arises (via the dielectric constant) from wave-vector structure in $V_{eff}({\bf q},\omega )$ at ${\bf q}=(\pi,\pi)$, which is associated with 2D Van Hove and local field effects. Our results, which are independent of the bandstructure, suggest that direct Coulomb intereactions are significant (when compared to the spin channel) and will, at the least, enhance any other underlying mechanism for $d_{x^2-y^2}$ wave pairing.