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Physical review. B, Condensed matter

Theory of photoemission and inverse photoemission in the presence of strong correlations: Application to high- Tc materials

C. A. R. Sá de Melo, Sebastian Doniach

Published Apr 1, 1990• 47 citations
Publisher

Abstract

We consider a single copper oxide plane with infinite Hubbard U on the copper sites and direct oxygen-oxygen and copper-oxygen overlaps as a model for high-${\mathit{T}}_{\mathit{c}}$ materials. Using a slave-boson representation, we find a region of parameter space with a charge-transfer-type metal-insulator transition at zero doping, i.e, half-filling in a mean-field limit. Performing a 1/N expansion we calculate the photoemission and inverse-photoemission spectra near the transition for both the n-type and p-type high-${\mathit{T}}_{\mathit{c}}$ materials using the sudden approximation.

DOI
10.1103/physrevb.41.6633

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We consider a single copper oxide plane with infinite Hubbard U on the copper sites and direct oxygen-oxygen and copper-oxygen overlaps as a model for high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials. Using a slave-boson representation, we find a region of parameter space with a charge-transfer-type metal-insulator transition at zero doping, i.e, half-filling in a mean-field limit. Performing a 1/N expansion we calculate the photoemission and inverse-photoemission spectra near the transition for both the n-type and p-type high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials using the sudden approximation.
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.
In this short communication we discuss results obtained for the single and multi-orbital Hubbard models within the mean-field-slave-boson description of correlated fermions on a square lattice. For appropriate parameter values the results can be used to mimic some of the normal state properties of the copper oxide systems. Results for the single and multi-orbital models differ in a very characteristic manner. In the single band case the phase diagram consists of metallic (U<Uc) and strongly correlated (U>Uc) regions, which are clearly seperated at half filling (Uc being the critical value of the Brinkman-Rice transition1)). Upon doping the transition between these two phases smoothes out and for large enough doping (δ>0.2, δ=1−n) the system behaves as a weakly correlated metal. In the multi-oibital case depending on the input energies for the orbitals the transition to the insulating state can be either of the Brinkman-Rice or the charge-transfer type. Similar to the single band case doping causes rapid loss of correlation effects. We tentatively conclude that the Kondo-type of effect is absent in the multi-orbital model.
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.
A systematic study is made of the t-J model as a working model for copper oxide high-Tc superconductors. The main focus is on the near-half- filling region (low hole concentrations) relevant to these materials. The theory of the magnetic polaron, which is a charge carrier traveling in an antiferromagnetic matrix, and the theory of antiferromagnetic ordering are discussed in a unified framework. The spin liquid state beyond the antiferromagnetic phase is examined. The Hamiltonian parameters – hole concentration phase diagram for the model is described and compared with that for the Hubbard model in the strong correlation limit. Two extensions of the t-J model, the t-t'-J model and the three-center interaction model, are discussed. Mostly analityc strong correlation techniques are employed in this review.
A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength UUU is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical UUU for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large UUU limit, intersite Coulomb repulsion VVV strongly suppresses the single-particle weight of the metallic state.
The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.