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Physical review. B, Condensed matter

Anomalous line shape of photoemission spectra in the underdoped high- Tc cuprates

Bumsoo Kyung

Published Jun 1, 1999• 1 citation
Publisher

Abstract

The line shape of photoemission spectra for underdoped cuprates is studied within the two-dimensional extended Hubbard model. Strong anisotropic scattering along the Fermi surface and the destruction of the Fermi surface near $(0,\ensuremath{\pi})$ are obtained for underdoped cuprates. These features are fully consistent with the recent angle-resolved photoemission experiments for underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ as well as with the recent QMC calculations.

DOI
10.1103/physrevb.59.14757

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The line shape of photoemission spectra for underdoped cuprates is studied within the two-dimensional extended Hubbard model. Strong anisotropic scattering along the Fermi surface and the destruction of the Fermi surface near (0,\ensuremathπ)(0,\ensuremath{\pi})(0,\ensuremathπ) are obtained for underdoped cuprates. These features are fully consistent with the recent angle-resolved photoemission experiments for underdoped Bi2Sr2CaCu2O8+\ensuremathδ{\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}Bi2​Sr2​CaCu2​O8+\ensuremathδ​ as well as with the recent QMC calculations.
The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function n(k)n(\mathbf{k})n(k), the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime (U=8)(U=8)(U=8) at low temperatures (T=0.01−−0.02)(T=0.01--0.02)(T=0.01−−0.02). At high doping (n=0.7)(n=0.7)(n=0.7), the system resembles an ordinary weakly interacting metal. At low doping (n=0.92)(n=0.92)(n=0.92), a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-Tc{T}_{c}Tc​ cuprates superconductors.
A consequence of strong antiferromagnetic correlations in models of high-Tc cuprates is the appearance in photoemission (PES) calculations of considerable more weight above the Fermi momentum pF{\rm {\bf p}_F }pF​ than expected for non-interacting electrons. This effect, first discussed by Kampf and Schrieffer (Phys. Rev. {\bf B 41}, 6399 (1990)) under the name of ``shadow bands'', is here analyzed in the two dimensional Hubbard and t-J models using Monte Carlo and exact diagonalization techniques. It is concluded that for underdoped compounds weight above pF{\rm {\bf p}_F }pF​ could be observable in experimental PES data, while in the overdoped regime it will be likely hidden in the experimental background. In the intermediate region the signal is weak. Our results are thus compatible with recent experimental data by Aebi et al. (Phys. Rev. Lett. {\bf 72}, 2757 (1994)) for Bi2212 at optimal doping. However, to definitely prove the existence of this effect in the cuprates, experiments in the underdoped regime are necessary.
We have investigated the evolution of the electronic properties of the t-t'-U Hubbard model with hole doping and temperature. Due to the shape of the Fermi surface, scattering from short wavelength spin fluctuations leads to strongly anisotropic quasi-particle scattering rates at low temperatures near half-filling. As a consequence, significant variations with momenta near the Fermi surface emerge for the spectral functions and the corresponding ARPES signals. This behavior is quite in contrast to the intermediate doping regime and we discuss the possible relevance of our results for the interpretation of photoemission spectra in cuprate superconductors at different hole doping levels.
We study the anomalous normal-state properties of a simple two-dimensional model whose ground state is a ddd-wave superconductor. Using a self-consistent, conserving formulation, we show that pairing correlations above Tc{T}_{c}Tc​ lead to the appearance of a highly anisotropic pseudogap in the electronic spectral function and the destruction of the Fermi surface. We discuss the similarities and differences between our results and angle-resolved photoemission spectroscopy experiments on underdoped cuprates.
Recently a pseudogap with d-wave symmetry was observed near the Fermi level in photoemission spectra of normal-state Bi2{\mathrm{Bi}}_{2}Bi2​Sr2{\mathrm{Sr}}_{2}Sr2​CaCu2{\mathrm{CaCu}}_{2}CaCu2​O8{\mathrm{O}}_{8}O8​ crystals. We demonstrate that an analogous pseudogap exists in the energy spectrum of the two-dimensional t-J model of cuprate perovskites. In agreement with experiment the magnitude of the pseudogap is 10--20 meV in underdoped crystals with hole concentration x\ensuremath{\lesssim}0.17 and the pseudogap disappears in optimally and overdoped crystals when x\ensuremath{\gtrsim}0.17. We demonstrate also that in the t-J model the overall energy spectrum near the Fermi level and the Fermi surface agree well with experimental observations.
We discuss spectra calculated for the two-dimensional Hubbard model in the intermediate coupling regime with the dynamical cluster approximation, which is a nonperturbative approach. We find a crossover from a normal Fermi liquid with a Fermi surface closed around the Brillouin-zone center at large doping to a non-Fermi liquid for small doping where the Fermi surface is holelike, closed around $M=(\ensuremath{\pi},\ensuremath{\pi}).$ The topology of the Fermi surface at low doping indicates a violation of Luttinger's theorem. We discuss different ways of presenting the spectral data to extract information about the Fermi surface. A comparison to recent experiments is presented.