Model calculation for electronic pairing in copper oxides

The interaction kernels due to charge and spin fluctuations are calculated in a simple tight-binding band model for the electronic structure of copper oxide planes. For a superconducting order parameter with d-wave symmetry, we find self-consistent solutions in which the pairing spin fluctuations dominate over the depairing charge fluctuations and large values of the critical temperature Tc are possible. By adding a small phonon contribution we get a small but finite isotope-effect coefficient (α) for Tc of about 100 K. We also find a large increase in α with decreasing Tc due to impurity scattering or band filling. For a suitable choice of parameters the α(Tc) curves are close to the experimental results