Strong Coupling Descriptions of High Temperature Superconductors: Electronic Attraction from a Repulsive Potential

We consider the effect of the nearest neighbour copper-oxygen repulsion, V, when coupled to the charge transfer resonances Cu2+ to Cu3+ and Cu2+ to Cu+ in the high temperature cuprate superconductors. This is done by deriving effective low energy Hamiltonians correct to second order in the copper-oxygen hybridisation. Only hole doping is considered. When Cu2+ to Cu3+ fluctuations dominate we derive an effective one-band model of `Zhang-Rice' singlets with a nearest neighbour repulsion between these singlets. When Cu2+ to Cu+ fluctuations dominate we find rich and complex behaviour. For large V we show that clusters of charge are more stable than isolated charges. On the other hand, for small V the Hamiltonian contains both weak attractive and repulsive two body potentials. Calculations on clusters indicate that the attractive potentials have the same correlations as the more dominate `single particle' terms suggesting the possibility of `s' wave pairing.