International Journal of Modern Physics B

ON THE THEORY OF THE HIGH-TcSUPERCONDUCTING MATERIALS

Peter Fulde

Published Jan 1, 1993• 0 citations

Abstract

Methods are described which can be used for an analytical description of the strong electron correlations in the planes of the Cu–O based high-Tc superconducting materials. One is a projection technique which is applied in order to calculate the photoelectron and inverse photoelectron spectra for the cases of half filling and hole doping of the Cu–O planes. Good agreement with the results of exact diagonalization of (CuO2)4 clusters is obtained, proving the usefulness of the method. Another one is the concept of string states which can be applied to study the t–J model. Also in this case a number of numerical findings can be reproduced and improved by this analytic method.

DOI: 10.1142/s0217979293000184

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International Journal of Modern Physics B

ON THE THEORY OF THE HIGH-TcSUPERCONDUCTING MATERIALS

Peter Fulde

Published Jan 1, 1993• 0 citations

Publisher

Abstract

DOI: 10.1142/s0217979293000184

Related papers

Electronic excitation spectra of the Emery model

Patrick Unger, Peter Fulde

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 ${\mathit{U}}_{\mathit{d}}$ 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 ( ${\mathrm{CuO}}_{2}$ ${)}_{4}$ cluster with periodic boundary conditions.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 ${\mathit{U}}_{\mathit{d}}$ 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 (${\mathrm{CuO}}_{2}$${)}_{4}$ cluster with periodic boundary conditions.

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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.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.

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Peter Fulde, Patrick Unger, Jun-ichi Igarashi

Until now, solids with strongly correlated electrons can be treated only by model Hamiltonians. Even then a calculation of spectral densities is not simple, because the strong Coulomb interactions prevent us from treating correlations perturbatively. We show that projection and partitioning techniques are a very valuable tool here. The method is applied to computations of the density of states of transition metals, in particular, Ni. Here, the band narrowing and the sattlite peak at 6 eV due to correlations are reproduced. A second application concerns the spectral density of doped and undoped Cu(SINGLE BOND)O planes which are part of the high-Tc superconducting materials. © 1997 John Wiley & Sons, Inc. J Quant Chem 63: 645–653, 1997Until now, solids with strongly correlated electrons can be treated only by model Hamiltonians. Even then a calculation of spectral densities is not simple, because the strong Coulomb interactions prevent us from treating correlations perturbatively. We show that projection and partitioning techniques are a very valuable tool here. The method is applied to computations of the density of states of transition metals, in particular, Ni. Here, the band narrowing and the sattlite peak at 6 eV due to correlations are reproduced. A second application concerns the spectral density of doped and undoped Cu(SINGLE BOND)O planes which are part of the high-Tc superconducting materials. © 1997 John Wiley & Sons, Inc. J Quant Chem 63: 645–653, 1997

International Journal of Quantum ChemistryJan 1, 19973 citations

{\mathit{U}}_{\mathit{d}}

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 (

{\mathrm{CuO}}_{2}

{)}_{4}

cluster with periodic boundary conditions.

The hole distribution within a

{\mathrm{CuO}}_{2}

plane, a common structural element of high-temperature superconductors, is investigated as a function of doping by holes. The correlated ground state of a three-band Hubbard model is found by making use of a local ansatz which includes local correlations between holes. It is found that doped holes have \ensuremath{\sim}70% oxygen character for the parameters determined from the local-density approximation, in agreement with experimental observations, while hole droplets on oxygen orbitals are formed for large copper-oxygen Coulomb repulsion,

{\mathit{U}}_{\mathit{d}\mathit{p}}

. All our results agree with those obtained from finite-cluster diagonalization.

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.

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.

{\mathrm{O}}_{2}

planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the $t\ensuremath{-}J$ model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular, abnormal features like the mid-infrared band of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$, the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.