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Physical review. B, Condensed matter

Doping dependence of high-energy spectral weights for the high- Tc cuprates

Henk J. Eskes, G. A. Sawatzky

Published Jan 1, 1991• 126 citations
Publisher

Abstract

In this paper we present calculations of the photo- and inverse photoemission spectra, and the O 1s and Cu 2p core-level spectra for the high-${\mathit{T}}_{\mathit{c}}$ materials, using a multiband Hubbard Hamiltonian. The spectra are obtained for small clusters containing two Cu atoms (${\mathrm{Cu}}_{2}$${\mathrm{O}}_{7}$ and ${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8}$) for the undoped, electron-doped, and hole-doped cases. In order to investigate the sensitivity of the spectra to cluster size and localized versus delocalized oxygen levels, a comparison is made with a (k-dependent) impurity approach and results from a ${\mathrm{CuO}}_{4}$ cluster. Special attention is paid to the doping dependence of the spectra and the low-energy states and to the redistribution of spectral weights upon doping.

DOI
10.1103/physrevb.43.119

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Physical review. B, Condensed matter•Apr 1, 1993•30 citations
In this paper we present calculations of the photo- and inverse photoemission spectra, and the O 1s and Cu 2p core-level spectra for the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials, using a multiband Hubbard Hamiltonian. The spectra are obtained for small clusters containing two Cu atoms ({\mathrm{Cu}}_{2}$${\mathrm{O}}_{7} and {\mathrm{Cu}}_{2}$${\mathrm{O}}_{8}) for the undoped, electron-doped, and hole-doped cases. In order to investigate the sensitivity of the spectra to cluster size and localized versus delocalized oxygen levels, a comparison is made with a (k-dependent) impurity approach and results from a CuO4{\mathrm{CuO}}_{4}CuO4​ cluster. Special attention is paid to the doping dependence of the spectra and the low-energy states and to the redistribution of spectral weights upon doping.
Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-Tc{\mathit{T}}_{\mathit{c}}Tc​) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.
We have analyzed experimental evidence for an anomalous transfer of spectral weight from high- to low-energy scales in both electron- and hole-doped cuprates as a function of doping. X-ray scattering, optical, and photoemission spectra are all found to show that the high-energy spectral weight decreases with increasing doping at a rate much faster than predictions of the large UUU-limit calculations. The observed doping evolution is however well described by an intermediate coupling scenario where the effective Hubbard UUU is comparable to the bandwidth. The experimental spectra across various spectroscopies are inconsistent with fixed-UUU exact diagonalization or quantum Monte Carlo calculations, and suggest a significant doping dependence of the effective UUU in the cuprates.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
We compare numerical results of O and Cu occupations and optical and magnetic excitations for the three-band Hubbard model in a Cu4{\mathrm{Cu}}_{4}Cu4​O8{\mathrm{O}}_{8}O8​ cluster, with those obtained with an effective Hamiltonian Heff{\mathit{H}}_{\mathit{e}\mathit{f}\mathit{f}}Heff​ in which the Cu-O hopping tpd{\mathit{t}}_{\mathit{p}\mathit{d}}tpd​ is eliminated by means of a canonical transformation. This transformation up to order tpd4{\mathit{t}}_{\mathit{p}\mathit{d}}^{4}tpd4​ is not quantitatively valid when the relevant energy differences are of the order of \ensuremath{\surd}8 tpd{\mathit{t}}_{\mathit{p}\mathit{d}}tpd​ or less. However, an Heff{\mathit{H}}_{\mathit{e}\mathit{f}\mathit{f}}Heff​ with the form of the second-order one, but which retains all higher-order terms contained in a CuO4{\mathrm{CuO}}_{4}CuO4​ (Cu2{\mathrm{Cu}}_{2}Cu2​O7{\mathrm{O}}_{7}O7​) cluster for zero or one added hole (one added electron) to the undoped system, leads to a very good agreement with the results using the full Hilbert space. This Heff{\mathit{H}}_{\mathit{e}\mathit{f}\mathit{f}}Heff​ makes possible the numerical study of the three-band Hubbard model for realistic parameters, using larger clusters.
An exact diagonalization technique on small lattices is used to calculate the single-particle spectral function A(k,\ensuremath{\omega}) for one- and three-band Hubbard models at various parameter values and doping rates, thereby examining the low-energy electronic structure (or in-gap state) of the doped CuO2{\mathrm{CuO}}_{2}CuO2​ plane in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting cuprates. It is illustrated that, by carrier doping, the dispersive state of the charge excitation gap at half filling undergoes a strongly momentum-dependent spectral-weight transfer, and evolves into the new state with a free-electron-like dispersion that forms the in-gap state characteristic of a large Fermi surface consistent with Luttinger's sum rule. The quasiparticlelike band narrowing observed is shown to depend sensitively on the parameter values and doping rate.
We calculate the photoemission and inverse photoemission spectra of holes in copper-oxygen planes, the characteristic structural unit of high-temperature superconductors. The computations are based on the extended Hubbard or Emery model in the limit of infinitely strong Coulomb repulsion Ud{\mathit{U}}_{\mathit{d}}Ud​ on copper sites. In order to evaluate the corresponding one-particle correlation functions the projection technique is applied, which is especially suitable for strongly correlated systems. Thereby the hole dynamics is restricted to a subspace of relevant operators, within which it can be treated exactly. In contrast to independent-particle approximations the excitation spectra show an energy gap at half-filling, which disappears when the system is doped with additional holes. Besides the insulator-to-metal transition the strong correlations lead also to a significant shift of spectral weight to states close to the Fermi energy when the hole concentration increases. Our results are in good agreement with the ones of exact diagonalization studies of the (CuO2{\mathrm{CuO}}_{2}CuO2​)4{)}_{4})4​ cluster with periodic boundary conditions.