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Physical review. B, Condensed matter

Charge collective modes and dynamic pairing in the three-band Hubbard model. II. Strong-coupling limit

Roberto Raimondi, Claudio Castellani, M. Grilli, Yunkyu Bang, Gabriel Kotliar

Published Feb 1, 1993• 53 citations
Publisher

Abstract

We analyze the dynamics of the charge degrees of freedom in the extended Hubbard model for the ${\mathrm{CuO}}_{2}$ planes in copper oxides in the strong-coupling limit. We analyze the behavior of the collective modes near the charge-transfer instability (CTI). The CTI is driven by an overdamped zero-sound mode when the Landau stability criterion ${\mathit{F}}_{0}^{\mathit{s}}$>-1 is violated due to the charge-transfer mode-mediated attraction. The divergence of the compressibility at the CTI requires a Maxwell construction, which determines a region of phase separation. Near the phase-separation boundary, at intermediate doping, the singlet Cooper coupling is attractive both in the s- and d-wave channels. In the strong-coupling limit the excitonic energy ${\mathrm{\ensuremath{\omega}}}_{\mathrm{exc}}$ is large and the energy scale for pairing is the Fermi energy itself.

DOI
10.1103/physrevb.47.3331

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We analyze the dynamics of the charge degrees of freedom in the extended Hubbard model for the CuO2{\mathrm{CuO}}_{2}CuO2​ planes in copper oxides in the strong-coupling limit. We analyze the behavior of the collective modes near the charge-transfer instability (CTI). The CTI is driven by an overdamped zero-sound mode when the Landau stability criterion F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​>-1 is violated due to the charge-transfer mode-mediated attraction. The divergence of the compressibility at the CTI requires a Maxwell construction, which determines a region of phase separation. Near the phase-separation boundary, at intermediate doping, the singlet Cooper coupling is attractive both in the s- and d-wave channels. In the strong-coupling limit the excitonic energy \ensuremathωexc{\mathrm{\ensuremath{\omega}}}_{\mathrm{exc}}\ensuremathωexc​ is large and the energy scale for pairing is the Fermi energy itself.
We analyze the role of the collective modes on the charge-transfer instability (CTI), phase separation, and the superconductivity in the extended Hubbard model. We show that, in the weak-coupling limit, the CTI appears when the zero-sound mode becomes unstable and the Landau stability criterion F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​>-1 is violated, due to a coupling to the charge-transfer exciton. We also study the frequency dependence of the effective interaction, mediated by the exchange of collective modes, between the quasiparticles.
The CuO2{\mathrm{CuO}}_{2}CuO2​ 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 Ud{\mathit{U}}_{\mathit{d}}Ud​, 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 CuO2{\mathrm{CuO}}_{2}CuO2​ lattice described by a three-band Hubbard model. For Ud{\mathit{U}}_{\mathit{d}}Ud​ 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}Ud{\mathit{U}}_{\mathit{d}}Ud​, 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 s∗{\mathit{s}}^{\mathrm{*}}s∗-wave channels near the antiferromagnetic boundary.
Exact diagonalisations of the extended two-band Hubbard model are performed. In the insulating regime it is shown that the nearest-neighbour copper-oxygen repulsion, V , leads to Frenkel excitons in the charge transfer gap at values of V of the order of copper-oxygen hybridisation, t . In the metallic regime it is shown that the static charge transfer and density-density correlation functions diverge as a function of V , indicating a charge transfer instability and phase separation. This is accompanied by a softening of the q → 0 mode of the dynamic correlation functions which is associated with the excitonic excitations responsible for the superconducting correlations observed in the proximity of the phase separation boundary described by C. Vermeulen et al. (C. Vermeulen et al. , Europhys. Lett. , 28 (1994) 653).
We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state.For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v 2Zt, |UD <2Zt) and strong coupling (v > 2Zt) limits.The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit.In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coułomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-frlling.The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined.It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction.Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an ``optimal'' value of the charge-transfer energy for the model where Tc{T}_{c}Tc​ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.
The extended Hubbard model for high temperature superconductors is studied for infinite systems in the strong coupling limit. The attractive interaction between added holes that has been noted for nearly degenerate copper and oxygen energy levels arises because the ground state is near an instability. Adding holes nucleates small regions of this unstable, infinitely compressible phase. Three distinct bound states of two holes occur in the strong coupling limit when double occupation is forbidden. In this limit, the attractive interaction results in phase separation rather than pairing when many holes are present. Perturbative calculations suggest that a pairing state is stable in a narrow parameter range as t increases.