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Phase diagrams for the strongly correlated three-band model of CuO2 planes. (Reannouncement with new availability information). Presentation paper

J. Charles Hicks, Andrei E. Ruckenstein, Gabriel Kotliar

Published Mar 1, 1991• 0 citations
OpenAlex

Abstract

A project scheme to linearize the equations of motion for the Hubbard model has been extended to a three-band model for CuO2 planes which includes an extended Hubbard interaction. The extended Hubbard term has been modified to allow for exchange effects within a large spin degeneracy (N) approximation. The 1/N expansion, modified to allow for exitonic effects, is used to study a range of parameter regimes to determine regions of phase separation, incompressibility, and superconducting instabilities.

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A project scheme to linearize the equations of motion for the Hubbard model has been extended to a three-band model for CuO2 planes which includes an extended Hubbard interaction. The extended Hubbard term has been modified to allow for exchange effects within a large spin degeneracy (N) approximation. The 1/N expansion, modified to allow for exitonic effects, is used to study a range of parameter regimes to determine regions of phase separation, incompressibility, and superconducting instabilities.
The ``fluctuation-exchange'' approximation, a Baym-Kadanoff theory used previously to treat the one-band Hubbard model, is used to investigate a three-band model for the CuO2{\mathrm{CuO}}_{2}CuO2​ planes in the cuprate superconductors. Attention is restricted to (a) nearest-neighbor copper-oxygen hopping and (b) a Hubbard-like Coulomb interaction on copper sites only. Orbital-occupancy factors are shown to be in good agreement with previous quantum simulation studies. An instability eigenvalue analysis confirms that, as in the one-band model, the most likely channel for superconductivity is a dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 singlet. The scale for onset of exponentially long-ranged antiferromagnetic correlations is compared with results for the one-band model, and the role of hybridization in reducing the effective Coulomb interaction is studied using a transformation to Wannier states.
Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.
We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
We calculate the effective interaction Weff between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a perturbative canonical transformation, to generate a two-body Hamiltonian. Then, we extend the results to all orders. The approach is exact in principle, and we obtain a close analytic expression including explicitly the effects of all virtual transitions to 4-body intermediate states. Our scheme naturally lends itself to embody off-site, inter-planar, phonon-mediated and other interactions which are not considered in the Hubbard model but may well be important. The result depends qualitatively on the symmetry of the two-hole state: 1 B2 and 1 A2 pairs are special, because the bare holes do not interact by the on-site repulsion (W=0 pairs). The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid; however Weff is repulsive for Triplet pairs. Bound two-hole states of the same nature were reported earlier in small cluster calculations by exact diagonalisation methods; only symmetric clusters are good models of the plane. Once Weff is known, the pair eigenfunction is determined by an integral equation. We present numerical estimates of the binding energy |∆ | of the pairs, which is in the physically interesting range of tens of meV if unscreened on-site repulsion parameters are used. 1 I.