Effective single-band Hubbard model for the cuprates: Coulomb interactions and apical oxygen

Starting with the three-band d-p model representing the high-Tc cuprates, we make a systematic reduction to an effective single-band model using a previously developed cell-perturbation method. In particular, we consider the effect of Coulomb repulsions on oxygen (Up) and between copper and oxygen (Vpd), and show that the resulting net Coulomb interaction between doped holes on neighbouring cells can be attractive due to locally enhanced pd hybridization, while this cannot occur for electrons. Extending to a five-band model, by including d3z2-r2 and apex pz orbitals, we show that there is, in addition to the usual Zhang-Rice singlet, a two-hole cell state which can be low in energy (depending on the proximity of the apicals), and may lead to a breakdown of the effective single-band model. ((orig.))