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Physical review. B, Condensed matter

Evolution of the in-gap state in high- Tc cuprates

Y. Ohta, Kenji Tsutsui, Wataru Koshibae, Tomohiro Shimozato, Sadamichi Maekawa

Published Dec 1, 1992• 69 citations
Publisher

Abstract

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 ${\mathrm{CuO}}_{2}$ plane in high-${\mathit{T}}_{\mathit{c}}$ 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.

DOI
10.1103/physrevb.46.14022

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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.
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.
We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (nh{\mathit{n}}_{\mathit{h}}nh​=1, one hole per CuO2{\mathrm{CuO}}_{2}CuO2​ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of nh{\mathit{n}}_{\mathit{h}}nh​=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 CuO2{\mathrm{CuO}}_{2}CuO2​ cluster.
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.
We study the evolution of the single-particle spectrum with electron doping in a scheme which adds multiple exchange of transverse spin excitations to the mean-field antiferromagnetic insulator. Away from half-filling small Fermi surface pockets appear first around the X points, and simultaneously new spectral weight grows in the insulating gap. With further doping the in-gap states develop the character of a renormalized quasiparticle band near the chemical potential. The essential features in momentum-energy space agree well with recent studies using angle-resolved photoemission spectroscopy on electron-doped cuprates. We interpret the origins and the nature of the in-gap states using a simple variational wave function.
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.
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.