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Physical Review Letters

Flat quasiparticle dispersion in the 2Dt-Jmodel

Elbio R. Dagotto, Alexander Nazarenko, Massimo Boninsegni

Published Aug 1, 1994• 209 citations
Publisher

Abstract

A model of weakly interacting hole quasiparticles is proposed to describe the normal state of the high temperature superconductors. The effect of strong correlations is contained in the dispersion relation of the holes, which is obtained accurately using a numerical technique and the t-J model on 8\ifmmode\times\else\texttimes\fi{}8, 12\ifmmode\times\else\texttimes\fi{}12, and 16\ifmmode\times\else\texttimes\fi{}16 clusters. Many-body effects induce anomalous quasiparticle flat bands similar to those observed in recent angle-resolved photoemission experiments. We also found that the Hall coefficient is in excellent quantitative agreement with experimental results for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$. Several other ``anomalous'' features of the cuprates can be explained with this model.

DOI
10.1103/physrevlett.73.728

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arXiv:cond-mat/9410039•Physical review. B, Condensed matter•Mar 1, 1996•23 citations
A model of weakly interacting hole quasiparticles is proposed to describe the normal state of the high temperature superconductors. The effect of strong correlations is contained in the dispersion relation of the holes, which is obtained accurately using a numerical technique and the t-J model on 8\ifmmode\times\else\texttimes\fi{}8, 12\ifmmode\times\else\texttimes\fi{}12, and 16\ifmmode\times\else\texttimes\fi{}16 clusters. Many-body effects induce anomalous quasiparticle flat bands similar to those observed in recent angle-resolved photoemission experiments. We also found that the Hall coefficient is in excellent quantitative agreement with experimental results for {\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}. Several other ``anomalous'' features of the cuprates can be explained with this model.
A model of weakly interacting hole quasiparticles is proposed to describe the normal state of the high temperature superconductors. The effect of strong correlations is contained in the dispersion relation of the holes, which is obtained accurately using a numerical technique and the t-J model on 12×1212\times 1212×12 clusters. Saddle-points generated by many-body effects induce quasiparticle flatflatflat bands similar to those observed in recent angle-resolved photoemission experiments. The near degeneracy between momentum states along the X−Y{\rm X-Y}X−Y direction is a hidden small energy scale in the problem, which produces a strongly temperature dependent Hall coefficient, as well as a large Fermi surface similar to those observed in the cuprates.
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.
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.
Self-energy corrections due to to fermion-magnon interaction are studied in the antiferromagnetic state of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}$ Hubbard model within the noncrossing approximation in the full UUU range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,{t}^{\ensuremath{'}},{t}^{\ensuremath{''}}$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states, etc. A finite-UUU induced classical dispersion term, absent in the $t\ensuremath{-}J$ model, is found to play an important role in suppressing the quasiparticle weight for states near k=(0,0)\mathbf{k}=(0,0)k=(0,0), as seen in cuprates. For intermediate UUU, the renormalized antiferromagnetic (AF) band gap is found to be nearly half of the classical value, and the weak-coupling limit is quite nontrivial due to strongly suppressed magnon amplitude. For finite ${t}^{\ensuremath{'}}$, the renormalized AF band gap is shown to vanish at a critical interaction strength Uc{U}_{c}Uc​, yielding a spin fluctuation driven first-order AF insulator--paramagnetic metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with angle-resolved photoemission spectroscopy data for Sr2CuO2Cl2{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​.
The Hall coefficient in the strongly correlated Fermi-liquid phase of the t-J model is studied for moderate hole concentrations. We find that the quasiparticle self-energy is strongly k dependent due to gauge-field interactions. It leads to corrections to the Fermi-surface curvature and to enhancement of the quasiparticle lifetime in the holelike region. We show that a systematic treatment of the strong local correlations to next to leading order in 1/N is sufficient to give rise to a sign change in the Hall coefficient. This effect occurs near 0.20 doping for J/t=0.2 and may be relevant to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials.
It is shown that the low-energy single-particle spectrum of the three-band Hubbard model at finite hole dopings agrees remarkably well with quantum Monte Carlo and experimental data within the framework of a conserving approximation including self-consistently the interaction with charge, spin, and particle-particle fluctuations. The dispersion of the quasiparticle peak is flat around the (\ensuremath{\pi},0), (0,\ensuremath{\pi}) points as observed in recent angle-resolved photoemission measurements. The significant reduction of the dispersion near the Fermi level is due to spin fluctuations, rather than being induced by band effects. \textcopyright{} 1996 The American Physical Society.