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Physical review. B, Condensed matter

Antiferromagnetic, charge-transfer, and pairing correlations in the three-band Hubbard model

Richard T. Scalettar, Douglas J. Scalapino, Robert L. Sugar, Steven R. White

Published Jul 1, 1991• 160 citations
Publisher

Abstract

The ${\mathrm{CuO}}_{2}$ sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The three-band Hubbard model with an on-site Cu Coulomb interaction ${\mathit{U}}_{\mathit{d}}$, which is large compared to the difference in energy \ensuremath{\varepsilon} between the O and Cu sites, provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a ${\mathrm{CuO}}_{2}$ lattice described by a three-band Hubbard model. For ${\mathit{U}}_{\mathit{d}}$ large compared with \ensuremath{\varepsilon}, and \ensuremath{\varepsilon} comparable to or larger than the bandwidth of the lower hole band, we find strong antiferromagnetic correlations and evidence for a charge-transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decrease with either hole or electron doping, and we see that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole-doped system exhibits a charge-transfer instability. As V is reduced, this is reflected as a peak in the charge-transfer susceptibility near \ensuremath{\varepsilon}+2V\ensuremath{\approxeq}${\mathit{U}}_{\mathit{d}}$, which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended ${\mathit{s}}^{\mathrm{*}}$-wave channels near the antiferromagnetic boundary.

DOI
10.1103/physrevb.44.770

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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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