Effective single-band models for the high-Tc cuprates. II. Role of apical oxygen

An effective single-band model for the cuprates is derived by a cell-perturbation method from a five-band model which includes d3z2-r2 orbitals on copper and pz orbitals on apical oxygen. In addition to the usual Zhang-Rice singlets of A1 symmetry, there are two-hole cell states of B1 symmetry, which can become low in energy and depend sensitively on the apical oxygen ions. Provided that hybridization with the apical oxygen orbital is sufficiently weak to permit reduction to a t-t'-J model, the main effect of the B1-symmetry states is to renormalize the effective next-nearest-neighbor hopping (t') of doped holes. This effect can be quite large and may even change the sign of t'. The variation of t' between various compounds due to differences in crystal structure is shown to correlate with Tcmax, the critical temperature at optimum doping, suggesting that t' may be a crucial parameter for the low-energy physics, which moreover differentiates between the various cuprates. The effective single-band model is shown to break down when the apex level approaches the in-plane oxygen level, and to describe that situation, which cannot be ruled out completely for the cuprates with present experimental evidence, we propose a specific minimal effective (two-band) model. copyright 1996 The American Physical Society