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Physical review. B, Condensed matter

Spectral function of holes in the Emery model

Patrick Unger, Peter Fulde

Published Dec 1, 1993• 49 citations
Publisher

Abstract

We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (${\mathit{n}}_{\mathit{h}}$=1, one hole per ${\mathrm{CuO}}_{2}$ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of ${\mathit{n}}_{\mathit{h}}$=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 ${\mathrm{CuO}}_{2}$ cluster.

DOI
10.1103/physrevb.48.16607

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We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (nh{\mathit{n}}_{\mathit{h}}nh​=1, one hole per CuO2{\mathrm{CuO}}_{2}CuO2​ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of nh{\mathit{n}}_{\mathit{h}}nh​=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 CuO2{\mathrm{CuO}}_{2}CuO2​ cluster.
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.
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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.
Strong coupling diagram technique equations are derived for hole Green’s functions of the three-band Hubbard model, which describes Cu–O planes of high-[Formula: see text] cuprates. The equations are self-consistently solved in the approximation, in which the series for the irreducible part in powers of the oxygen–copper hopping constant is truncated to two lowest-order terms. For parameters used for hole-doped cuprates, the calculated energy spectrum consists of lower and upper Hubbard subbands of predominantly copper nature, oxygen bands with a small admixture of copper states and the Zhang–Rice states of mixed nature, which are located between the lower Hubbard subband and oxygen bands. The spectrum contains also pseudogaps near transition frequencies of Hubbard atoms on copper sites.
Calculations of the single-particle spectral function for the two-band Hubbard model as a function of doping and nearest-neighbor Coulomb repulsion are performed on finite-size clusters. It is shown that for hole doping the effect of the nearest-neighbor Coulomb repulsion leads to the effective pinning of the Fermi energy, and to the creation of new states in the charge-transfer gap. For electron doping, however, the model behaves as a one-band Hubbard model with the Fermi energy moving into the conduction band. The results of this calculation are in qualitative agreement with some of the spectroscopic studies of the electronic structure at the Fermi energy of the high-temperature cuprate superconductors.
The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U . The concentration dependence of the Fermi surface strongly depends on hopping to second ( t ′) and third ( t ″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.