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arXiv:1305.7275 · Physical Review Letters

Phase Diagram of a Three-Orbital Model for High- Tc Cuprate Superconductors

Cédric Weber, Thierry Giamarchi, Chandra Mohan Varma

Published Mar 18, 2014• 60 citations
arXivHTMLPDF

Abstract

We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.

DOI
10.1103/physrevlett.112.117001

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We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.
The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d − p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of the antiferromagnetic state by changing the band parameters such as the hole number, level difference Δ d p between d and p electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when Δ d p decreases and the pure d -wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate x contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.
The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d-p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of antiferromagnetic state by changing the band parameters such as the hole number, level difference ΔdpΔ_{dp}Δdp​ between ddd and ppp electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when ΔdpΔ_{dp}Δdp​ decreases and the pure ddd-wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate xxx contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.
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.
The competition between ddd-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc{T}_{c}Tc​ cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte Carlo and experimental data, we verify that the low-energy excitations in a strongly correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at high (both hole and electron) doping.
Abstract We investigate the ground state of the two-dimensional three-band d-p model for for high-temperature superconductors on the basis of a variational Monte Carlo method. We employ an optimization variational Monte Carlo method that we have developed recently. The many-body wave function is improved beyond the Gutzwiller ansatz by adopting the wave function in the form ψ = exp(−S)ψG where ψG represents the Gutzwiller function and S is a kinetic operator. The strong magnetic correlation and also superconductivity (SC) are induced by the on-site Coulomb repulsive interaction. It is important to clarify the phase diagram that includes superconductive phase and antiferromagnetic phase. We show the phase diagram to show the antiferromagnetic region in the parameter space. High-temperature superconductivity may occur in the strongly correlated region near the antiferromagnetic boundary.
With the high-Tc cuprates in mind, properties of correlated d-wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer (t-t’-U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime (U>W, U: onsite correlation strength, W: band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U=Uco∼W. For U<Uco, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U>Uco (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.