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arXiv:cond-mat/0507564 · Journal of the Physical Society of Japan

Kink Structure in the Quasiparticle Band of Doped Hubbard Systems

Yoshiro Kakehashi, Peter Fulde

Published Sep 15, 2005• 11 citations
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Abstract

By making use of the self-consistent projection operator method with high-momentum and high-energy resolutions, we find a kink structure in the quasiparticle excitation spectrum of the two-dimensional Hubbard model in the underdoped regime. The kink is caused by a mixing between the quasiparticle state and excitations with short-range antiferromagnetic order. We suggest that this might be the origin of the strong concentration dependence of the 'kink' found in La_{2-x}Sr_{x}CuO_{4} (x=0.03-0.07).

DOI
10.1143/jpsj.74.2397

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By making use of the self-consistent projection operator method with high-momentum and high-energy resolutions, we find a kink structure in the quasiparticle excitation spectrum of the two-dimensional Hubbard model in the underdoped regime. The kink is caused by a mixing between the quasiparticle state and excitations with short-range antiferromagnetic order. We suggest that this might be the origin of the strong concentration dependence of the 'kink' found in La_{2-x}Sr_{x}CuO_{4} (x=0.03-0.07).
Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-TcT_{\rm c}Tc​ cuprates.
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.
Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy ${\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$ of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-Tc{T}_{c}Tc​ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.
Momentum-dependent excitation spectra of the two-dimensional Hubbard model on a square lattice have been investigated at zero temperature on the basis of the full self-consistent projection operator method in order to clarify nonlocal effects of electron correlations on the spectra. Intersite antiferromagnetic correlations are found to cause shadow bands and enhance the Mott-Hubbard splittings near the half-filling. Furthermore, nonlocal excitations are shown to move the critical doping concentration δ h *, at which the singular quasiparticle peak is located just on the Fermi level, from δ h * = 0.153 (the single-site value) to δ h * = 0.123. The latter suggests the occurrence of an instability such as the stripe at δ h * = 1/8.
A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is Ek{\mathit{E}}_{\mathit{k}}Ek​\ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.
On the basis of quantum Monte Carlo simulations of the two-dimensional Hubbard model which cover the doping range from the underdoped to the overdoped regime, we find that the single-particle spectral weight $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ qualitatively reproduces both the momentum ( ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ symmetry) and doping dependence of the pseudogap as found in photoemission experiments. The drastic doping dependence of the spin response ${\ensuremath{\chi}}_{s}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$, which is sharp in both $\stackrel{\ensuremath{\rightarrow}}{q}[\ensuremath{\approx}(\ensuremath{\pi},\ensuremath{\pi})]$ and $\ensuremath{\omega}$ in the underdoped regime but broad and structureless otherwise, identifies remnants of the antiferromagnetic order as the driving mechanism behind the pseudogap and its evolution with doping.