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Physical review. B, Condensed matter

Doping dependence of hole distribution in CuO2 planes of high- Tc superconductors: Local ansatz versus exact results

Jacek Dutka, Andrzej M. Oleś

Published Jul 1, 1990• 21 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.42.105

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The hole distribution within a CuO2{\mathrm{CuO}}_{2}CuO2​ 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, Udp{\mathit{U}}_{\mathit{d}\mathit{p}}Udp​. All our results agree with those obtained from finite-cluster diagonalization.
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.
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.
We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale two-dimensional tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $\ensuremath{\delta}\ensuremath{\sim}0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting ddd-wave superconductivity in the doping range $0.15\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, while at smaller doping around $\ensuremath{\delta}\ensuremath{\sim}1/8$ we find a strong competition between superconducting and nonsuperconducting stripes, including also pair density-wave states with an alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.
Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high-transition temperature cuprate superconductors, stripes are widely suspected to exist in a fluctuating form. We used numerically exact determinant quantum Monte Carlo calculations to demonstrate dynamical stripe correlations in the three-band Hubbard model, which represents the local electronic structure of the copper-oxygen plane. Our results, which are robust to varying parameters, cluster size, and boundary conditions, support the interpretation of experimental observations such as the hourglass magnetic dispersion and the Yamada plot of incommensurability versus doping in terms of the physics of fluctuating stripes. These findings provide a different perspective on the intertwined orders emerging from the cuprates' normal state.
We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.