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arXiv:cond-mat/9812325 · Physical review. B, Condensed matter

Angle-resolved Cu and O photoemission intensities in CuO2 planes

J. Eroles, C. D. Batista, Armando A. Aligia

Published Jun 1, 1999• 12 citations
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Abstract

Using a mapping from the three-band extended Hubbard model for cuprate superconductors into a generalized $t\ensuremath{-}J$ model, and exact diagonalization of the latter in a $4\ifmmode\times\else\texttimes\fi{}4$ cluster, we determine the quasiparticle weight for destruction of Cu or O electrons with definite wave vector k. We also derive an approximate but accurate analytical expression which relates the O intensity with the quasiparticle weight in the generalized $t\ensuremath{-}J$ model. The k dependence of Cu and O intensities is markedly different. In particular the O intensity vanishes for $k=(0,0).$ Our results are relevant for the interpretation of angle-resolved photoemission experiments.

DOI
10.1103/physrevb.59.14092

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Using a mapping from the three-band extended Hubbard model for cuprate superconductors into a generalized t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model, and exact diagonalization of the latter in a 4\ifmmode×\else\texttimes\fi44\ifmmode\times\else\texttimes\fi{}44\ifmmode×\else\texttimes\fi4 cluster, we determine the quasiparticle weight for destruction of Cu or O electrons with definite wave vector k. We also derive an approximate but accurate analytical expression which relates the O intensity with the quasiparticle weight in the generalized t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. The k dependence of Cu and O intensities is markedly different. In particular the O intensity vanishes for k=(0,0).k=(0,0).k=(0,0). Our results are relevant for the interpretation of angle-resolved photoemission experiments.
Using the self-consistent Born approximation, and the corresponding wave function of the magnetic polaron, we calculate the quasiparticle weight corresponding to destruction of a real electron (in contrast to creation of a spinless holon), as a function of wave vector for one hole in a generalized t-J model and the strong-coupling limit of a generalized Hubbard model. The results are in excellent agreement with those obtained by exact diagonalization of a sufficiently large cluster. Only the Hubbard weight compares very well with photoemission measurements in Sr2{\mathrm{Sr}}_{2}Sr2​CuO2{\mathrm{CuO}}_{2}CuO2​Cl2{\mathrm{Cl}}_{2}Cl2​.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on La1.28Nd0.6Sr0.12CuO4.{\mathrm{La}}_{1.28}{\mathrm{Nd}}_{0.6}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}.La1.28​Nd0.6​Sr0.12​CuO4​.
The momentum dispersion of the peak structure of the single-particle spectral weight A(p,\ensuremath{\omega}) of the two-dimensional Hubbard model is discussed. Using results obtained from Monte Carlo simulations on lattices up to 12\ifmmode\times\else\texttimes\fi{}12 in size, we determine the low-lying quasiparticle dispersion relation. This dispersion relation is anomalously flat near the (\ensuremath{\pi},0) and (0,\ensuremath{\pi}) points of the Brillouin zone, similar to the results of recent angular resolved photoemission measurements of the hole-doped cuprates. We argue that the generic nature of the quasiparticle dispersion relation observed in these materials arises from the strong Coulomb interaction and reflects the hole-spin correlations rather than the one-electron interactions which customarily determine the band structure.
We study the Cu and O spectral density of states and the optical conductivity of CuO2{}_{2}2​ planes using an effective generalized one-band Hubbard model derived from the extended three-band Hubbard model. We solve exactly a square cluster of 10 unit cells and average the results over all possible boundary conditions, which leads to smooth functions of frequency. Upon doping, the Fermi energy jumps to Zhang-Rice states which are connected to the rest of the valence band (in contrast to an isolated band in the middle of the gap). The transfer of spectral weight depends on the parameters of the original three-band model not only through the one-band effective parameters but also through the relevant matrix elements. We discuss the evolution of the gap upon doping. The optical conductivity of the doped system shows a mid-infrared peak due to intraband transitions, a pseudogap, and a high-frequency part related to interband transitions. Its shape and integrated weight up to a given frequency (including the Drude weight) agree qualitatively with experiments in the cuprates for low to moderate doping levels, but significant deviations exist for doping x>0.3x>0.3x>0.3.
For the calculation of charge excitations as those observed in, e.g., photoemission spectroscopy or in electron-energy-loss spectroscopy, a correct description of ground-state charge properties is essential. In strongly correlated systems like the undoped cuprates this is a highly nontrivial problem. In this paper we derive a nonperturbative analytical approximation for the ground state of the three-band Hubbard model on an infinite, half-filled CuO2{\mathrm{CuO}}_{2}CuO2​ plane. By comparison with projector quantum Monte Carlo calculations it is shown that the resulting expressions correctly describe the charge properties of the ground state. Relations to other approaches are discussed. The analytical ground state preserves size consistency and can be generalized for other geometries, while still being both easy to interpret and to evaluate.
In many cases the standard perturbation approach appears to be too simple to describe precisely the angle-resolved photoemission spectrum of a strongly correlated electron system. In particular, to describe the momentum asymmetry observed in the photoemission spectra of high-Tc{T}_{c}Tc​ cuprates, a phenomenological approach based on an extremely correlated Fermi-liquid model has been recently introduced. Here we analyze the general structure of the Green's function of quasiparticles in strongly correlated electron systems and stress that it is defined not only by the self-energy of Hubbard quasiparticles but also by a strength operator. The latter leads to an additional odd momentum contribution to the spectral function and alone can explain the observed asymmetry. So, the asymmetry of the angle-resolved photoemission spectra can be a measure of the strength of electron correlations in materials.