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

Abstract

An effective single-band model for the cuprates is derived by a cell-perturbation method from a five-band model which includes {ital d}{sub 3{ital z}{sup 2}{minus}{ital r}{sup 2}} orbitals on copper and {ital p}{sub {ital z}} orbitals on apical oxygen. In addition to the usual Zhang-Rice singlets of {ital A}{sub 1} symmetry, there are two-hole cell states of {ital B}{sub 1} 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 {ital t}-{ital t}{sup {prime}}-{ital J} model, the main effect of the {ital B}{sub 1}-symmetry states is to renormalize the effective next-nearest-neighbor hopping ({ital t}{sup {prime}}) of doped holes. This effect can be quite large and may even change the sign of {ital t}{sup {prime}}. The variation of {ital t}{sup {prime}} between various compounds due to differences in crystal structure is shown to correlate with {ital T}{sub {ital c}}{sup max}, the critical temperature at optimum doping, suggesting that {ital t}{sup {prime}} 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 approachesmore » 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} {ital 1996 The American Physical Society.}« less