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Physical review. B, Condensed matter

Spectral-weight transfer in effective single-band models for the high- Tc cuprates

L. F. Feiner

Published Dec 1, 1993• 25 citations
Publisher

Abstract

The low-energy physics of the Emery model, representing the high-${\mathit{T}}_{\mathit{c}}$ cuprates, can be understood by separating intracell interference within ${\mathrm{CuO}}_{4}$ cells from intercell correlations described by an effective single-band Hubbard model. This decomposition explains the anomalous transfer of spectral intensity from the high- to the low-energy scale, the asymmetry between electron and hole doping, and the breakdown of low-energy sum rules. These features are related to the existence of an antibound charge transfer exciton band, are are very sensitive to the strength of the Coulomb repulsion ${\mathit{U}}_{\mathit{d}}$.

DOI
10.1103/physrevb.48.16857

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The low-energy physics of the Emery model, representing the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates, can be understood by separating intracell interference within CuO4{\mathrm{CuO}}_{4}CuO4​ cells from intercell correlations described by an effective single-band Hubbard model. This decomposition explains the anomalous transfer of spectral intensity from the high- to the low-energy scale, the asymmetry between electron and hole doping, and the breakdown of low-energy sum rules. These features are related to the existence of an antibound charge transfer exciton band, are are very sensitive to the strength of the Coulomb repulsion Ud{\mathit{U}}_{\mathit{d}}Ud​.
We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and ddd-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.
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Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-Tc{\mathit{T}}_{\mathit{c}}Tc​) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.
In this paper we study the spectral-weight transfer from the high- to the low-energy scale by means of exact diagonalization of finite clusters for the Mott-Hubbard and charge-transfer model. We find that the spectral-weight transfer is very sensitive to the hybridization strength as well as to the amount of doping. This implies that the effective number of low-energy degrees of freedom is a function of the hybridization and therefore of the volume and temperature. In this sense it is not possible to define a Hamiltonian which describes the low-energy-scale physics unless one accepts an effective nonparticle conservation.
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Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high- T c superconductivity. Recent measurements of the dynamical spin structure factor (DSF) in cuprate ladder compounds have indicated the presence of an additional, attractive term in the single-band Hubbard model, potentially originating from electron-phonon interactions. Here, we demonstrate that similar DSF features can also be captured by t − J descriptions with a smaller attractive term. Motivated by this observation, we systematically investigate the strength and origin of different contributions to the single-band Hamiltonians by downfolding either from the three-band Emery model or the electron-phonon coupled Hubbard-Holstein model. For one-dimensional systems, we find that the extended versions of both single-band descriptions can reproduce the experimentally observed DSF signatures. Finally, we extend our analysis to two dimensions by comparing two-hole correlation functions for the different single-band models. Our results provide new insights into the long-standing question of which single-band Hamiltonian can capture the essential physics of cuprates.