alexa Effective single-band models for the high-Tc cuprates. I. Coulomb interactions


Journal of Astrophysics & Aerospace Technology

Author(s): L F Feiner, J H Jefferson, R Raimondi

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Starting with the three-band extended Hubbard model (or d-p model) widely used to represent the CuO2 planes in the high-Tc cuprates, we make a systematic reduction to an effective single-band model using a previously developed cell-perturbation method. The range of parameters for which this mapping is a good approximation is explored in the full Zaanen-Sawatzky-Allen diagram (copper Coulomb repulsion Ud versus charge-transfer energy ɛ), together with an investigation of the validity of a further mapping to an effective charge-spin (t-J-V) model. The variation of the effective single-band parameters with the parameters of the underlying multi-band model is investigated in detail, and the parameter regime where the model represents the high-Tc cuprates is examined for specific features that might distinguish it from the general case. In particular, we consider the effect of Coulomb repulsions on oxygen (Up) and between copper and oxygen (Vpd). We find that the reduction to an effective single-band model is generally valid for describing the low-energy physics, and that Vpd and Up (unless unrealistically large) actually slightly improve the convergence of the cell-perturbation method. Unlike in the usual single-band Hubbard model, the effective intercell hopping and Coulomb interactions are different for electrons and holes. We find that this asymmetry, which vanishes in the extreme Mott-Hubbard regime (Ud≪ɛ), is quite appreciable in the charge-transfer regime (Ud≳ɛ), particularly for the effective Coulomb interactions. We show that for doped holes (forming Zhang-Rice singlets) on neighboring cells the interaction induced by Vpd can even be attractive due to locally enhanced pd hybridization, while this cannot occur for electrons. The Coulomb interaction induced by Up is always repulsive; in addition Up gives rise to a ferromagnetic spin-spin interaction which opposes antiferromagnetic superexchange. We show that for hole-doped systems this leads to a subtle cancellation of attractive and repulsive contributions, due to antiferromagnetic and charge-polarization effects, to the net static interaction in a charge-spin (t-J-V) model, and we discuss the significance of this result. The asymmetry in the ee, hh, and eh effective hopping parameters can be particularly large for next-nearest neighbors. Specializing to cuprate parameters, we find that the asymmetry in the nearest-neighbor hopping parameters almost vanishes (accidentally), while the next-nearest-neighbor hopping parameter t′ is close to zero for electrons but is appreciable for holes (t′≊-0.06 eV). The effective Coulomb interaction between doped holes is found to be repulsive, and even slightly larger than for electrons. All the underlying d-p parameters make significant contributions to the effective interactions and it is shown that certain approximations, such as Ud=∞ and tpp=0, can be qualitatively incorrect.

This article was published in PHYSICAL REVIEW B and referenced in Journal of Astrophysics & Aerospace Technology

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