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Physical review. B, Condensed matter

Quasiparticle dispersion in the cuprate superconductors and the two-dimensional Hubbard model

N. Bulut, Douglas J. Scalapino, Steven R. White

Published Sep 1, 1994• 129 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.50.7215

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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.
Employing dynamical cluster quantum Monte Carlo calculations we show that the single-particle spectral weight A(k,omega) of the one-band two-dimensional Hubbard model displays a high-energy kink in the quasiparticle dispersion followed by a steep dispersion of a broad peak similar to recent angle-resolved photoemission spectroscopy results reported for the cuprates. Based on the agreement between the Monte Carlo results and a simple calculation which couples the quasiparticle to spin fluctuations, we conclude that the kink and the broad spectral feature in the Hubbard model spectra is due to scattering with damped high-energy spin fluctuations.
The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.
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 ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. Several other ``anomalous'' features of the cuprates can be explained with this model.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/kTc{\mathit{kT}}_{\mathit{c}}kTc​\ensuremath{\simeq}4.
On the basis of quantum Monte Carlo results the evolution of the spectral weight $A(\mathbf{k},\ensuremath{\omega})$ of the two-dimensional Hubbard model is studied from insulating to metallic behavior. As observed in recent photoemission experiments for cuprates, the electronic excitations display essentially doping-independent features; a quasiparticlelike dispersive narrow band of width of the order of the exchange interaction JJJ and a broad valence- and conduction-band background. The continuous evolution is traced back to one and the same many-body origin: the doping-dependent antiferromagnetic spin-spin correlation.
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.