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Modern Physics Letters B

LINEAR EXCITATIONS AROUND BROKEN-SYMMETRY MEAN-FIELD STATES: DOPING STATES IN THE COPPER OXIDES

Kenji Yonemitsu, A. R. Bishop, J. Lorenzana

Published Mar 10, 1993• 1 citation
Publisher

Abstract

Nonlinear doping states in Peierls–Hubbard models are investigated through response functions in magnetic, optical and vibronic channels. A random phase approximation is used for their analysis on the basis of totally unrestricted Hartree–Fock solutions, which in general have broken symmetries. The validity of the present method is first discussed through a comparison with known exact results for a two-site two-electron system. Then this method is applied to a two-dimensional three-band system with one additional hole relative to stoichiometry, for modeling the lightly doped copper oxides. New excitation modes are induced by doping and observed in the different channels of response functions. These doping-induced modes distinguish between various doping states and helpful for the identification of doping states in specific materials.

DOI
10.1142/s0217984993000369

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Nonlinear doping states in Peierls–Hubbard models are investigated through response functions in magnetic, optical and vibronic channels. A random phase approximation is used for their analysis on the basis of totally unrestricted Hartree–Fock solutions, which in general have broken symmetries. The validity of the present method is first discussed through a comparison with known exact results for a two-site two-electron system. Then this method is applied to a two-dimensional three-band system with one additional hole relative to stoichiometry, for modeling the lightly doped copper oxides. New excitation modes are induced by doping and observed in the different channels of response functions. These doping-induced modes distinguish between various doping states and helpful for the identification of doping states in specific materials.
All the linear excitations are calculated in the random-phase approximation around a doped inhomogeneous Hartree-Fock state as well as the undoped uniform antiferromagnetic state in the one-dimensional Hubbard model. Upon doping, shape modes appear, localized around an introduced hole, as well as some ``shake-off'' branches related to combinations of local and extended Hartree-Fock orbitals. These modes are in addition to spin wave and ultragap branches in the pure antiferromagnetic state. Some characteristics of the shape modes are similar to bare processes in the t-t'-J model derived from the Hubbard model at strong coupling. Spectral weights in different susceptibility channels are calculated and shown to have peaks in low-energy regions, arising from specific shape modes.
A field theory for the strong-coupling limit of a one-dimensional copper-oxide model is obtained from a weak-coupling point of view. Complementary aspects of strong correlations and band motion are incorporated in a natural way. Doping induces soliton or antisoliton charge excitations into a state with explicity broken chiral symmetry. The solitons or antisolitons have divergent superconductive pairing-correlation functions and various properties reminiscent of doped holes or electrons in high-temperature superconductors.
Recent numerical results for the single-particle spectral function and optical conductivity of the two-dimensional Hubbard and t−J models are reviewed. Already for two holes in systems of sixteen to twenty sites (≥ 10% doping) a large electronic Fermi surface, compatible with Luttinger’s theorem, is observed. The full single-particle Green’s function is examined, and is shown to exhibit quasiparticle-like behavior, with dispersion consistent with the band structure of the non-interacting limit, and band width scaling approximately as J for J smaller than t. The optical conductivity of the Hubbard and t−J models is shown to have many features in common with recent experiments on copper oxide superconductors. The importance of the often neglected 3-site terms which arise in the derivation of the t−J model from the Hubbard model for optical properties is discussed.
The three-band model relevant to high-temperature copper-oxide superconductors is solved using single-site dynamical mean field theory and a tight-binding parametrization of the copper and oxygen bands. For a band filling of one hole per unit cell the metal/charge-transfer-insulator phase diagram is determined. The electron spectral function, optical conductivity, and quasiparticle mass enhancement are computed as functions of electron and hole doping for parameters such that at one hole per cell the paramagnetic phase is insulating and for parameters such that at one hole per unit cell the paramagnetic phase is metallic. The optical conductivity is computed using the Peierls phase approximation for the optical matrix elements. The calculation includes the physics of ``Zhang-Rice singlets.'' The effects of antiferromagnetism on the magnitude of the gap and the relation between correlation strength and doping-induced changes in state density are determined. Three-band and one-band models are compared. The two models are found to yield quantitatively consistent results for all energies less than about 4 eV including energies in the vicinity of the charge-transfer gap. Parameters on the insulating side of the metal/charge-transfer insulator phase boundary lead to gaps which are too large and near-gap conductivities which are too small relative to data. The results place the cuprates clearly in the intermediate correlation regime, on the paramagnetic metal side of the metal/charge-transfer insulator phase boundary.
As a convenient qualitative approach to strongly correlated electronic systems, an inhomogeneous Hartree-Fock plus random-phase approximation is applied to response functions for the two-dimensional multiband Hubbard model for cuprate superconductors. A comparison of the results with those obtained by exact diagonalization by Wagner, Hanke, and Scalapino [Phys. Rev. B 43, 10 517 (1991)] shows that overall structures in optical and magnetic particle-hole excitation spectra are well reproduced by this method. This approach is computationally simple, retains conceptual clarity, and can be calibrated by comparison with exact results on small systems. Most importantly, it is easily extended to larger systems and straightforward to incorporate additional terms in the Hamiltonian, such as electron-phonon interactions, which may play a crucial role in high-temperature superconductivity.
We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.