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arXiv:1011.2141 · Physical Review B

Failure of t−J models in describing doping evolution of spectral weight in x-ray scattering, optical, and photoemission spectra of cuprates

R.S. Markiewicz, Tanmoy Das, Arun Bansil

Published Dec 1, 2010• 25 citations
arXivHTMLPDF

Abstract

We have analyzed experimental evidence for an anomalous transfer of spectral weight from high- to low-energy scales in both electron- and hole-doped cuprates as a function of doping. X-ray scattering, optical, and photoemission spectra are all found to show that the high-energy spectral weight decreases with increasing doping at a rate much faster than predictions of the large $U$-limit calculations. The observed doping evolution is however well described by an intermediate coupling scenario where the effective Hubbard $U$ is comparable to the bandwidth. The experimental spectra across various spectroscopies are inconsistent with fixed-$U$ exact diagonalization or quantum Monte Carlo calculations, and suggest a significant doping dependence of the effective $U$ in the cuprates.

DOI
10.1103/physrevb.82.224501

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We have analyzed experimental evidence for an anomalous transfer of spectral weight from high- to low-energy scales in both electron- and hole-doped cuprates as a function of doping. X-ray scattering, optical, and photoemission spectra are all found to show that the high-energy spectral weight decreases with increasing doping at a rate much faster than predictions of the large UUU-limit calculations. The observed doping evolution is however well described by an intermediate coupling scenario where the effective Hubbard UUU is comparable to the bandwidth. The experimental spectra across various spectroscopies are inconsistent with fixed-UUU exact diagonalization or quantum Monte Carlo calculations, and suggest a significant doping dependence of the effective UUU in the cuprates.
Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-Tc{\mathit{T}}_{\mathit{c}}Tc​) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for Sr2CuO2Cl2{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation T=t/3T=t/3T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density 〈n〉〈n〉〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from (0,0)(0,0)(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended sss-wave character is found to compete with the ddd wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as 〈n〉〈n〉〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.
Using a recently developed perturbative approach, which considers Hubbard operators as fundamental excitations, we have performed electronic self-energy and spectral function calculations for the $t\text{\ensuremath{-}}J$ model on the square lattice. We have found that the spectral functions along the Fermi surface are isotropic, even close to the critical doping where the ddd density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight ZZZ was obtained. ZZZ decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.
An exact diagonalization technique on small lattices is used to calculate the single-particle spectral function A(k,\ensuremath{\omega}) for one- and three-band Hubbard models at various parameter values and doping rates, thereby examining the low-energy electronic structure (or in-gap state) of the doped CuO2{\mathrm{CuO}}_{2}CuO2​ plane in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting cuprates. It is illustrated that, by carrier doping, the dispersive state of the charge excitation gap at half filling undergoes a strongly momentum-dependent spectral-weight transfer, and evolves into the new state with a free-electron-like dispersion that forms the in-gap state characteristic of a large Fermi surface consistent with Luttinger's sum rule. The quasiparticlelike band narrowing observed is shown to depend sensitively on the parameter values and doping rate.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
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-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials, using a multiband Hubbard Hamiltonian. The spectra are obtained for small clusters containing two Cu atoms (Cu2{\mathrm{Cu}}_{2}Cu2​O7{\mathrm{O}}_{7}O7​ and Cu2{\mathrm{Cu}}_{2}Cu2​O8{\mathrm{O}}_{8}O8​) 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 CuO4{\mathrm{CuO}}_{4}CuO4​ 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.