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arXiv:cond-mat/0010448 · Journal of the Physical Society of Japan

Pseudogap Induced by Antiferromagnetic Spin Correlation in High-Temperature Superconductors

Tôru Sakai, Yoshinori Takahashi

Published Jan 15, 2001• 14 citations
arXivHTMLPDF

Abstract

The pseudogap phenomena observed on cuprate high temperature superconductors are investigated based on the exact diagonalization method on the finite cluster t-J model. The results show the presence of the gap-like behavior in the temperature dependence of various magnetic properties; the NMR relaxation rate, the neutron scattering intensity and the static susceptibility. The calculated spin correlation function indicates that the pseudogap behavior arises associated with the development of the antiferromagnetic spin correlation with decreasing the temperature. The numerical results are presented to clarify the model parameter dependence, that covers the realistic experimental situation. The effect of the next-nearest neighbor hopping $t'$ is also studied.

DOI
10.1143/jpsj.70.272

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The pseudogap phenomena observed on cuprate high temperature superconductors are investigated based on the exact diagonalization method on the finite cluster t-J model. The results show the presence of the gap-like behavior in the temperature dependence of various magnetic properties; the NMR relaxation rate, the neutron scattering intensity and the static susceptibility. The calculated spin correlation function indicates that the pseudogap behavior arises associated with the development of the antiferromagnetic spin correlation with decreasing the temperature. The numerical results are presented to clarify the model parameter dependence, that covers the realistic experimental situation. The effect of the next-nearest neighbor hopping t′t't′ is also studied.
We present reliable many-body calculations for the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature-dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering, and for the phase diagram.
The pseudogap in the cuprate high-temperature superconductors was discovered as a suppression of the Knight shift and spin relaxation time measured in nuclear magnetic resonance (NMR) experiments. However, theoretical understanding of this suppression in terms of the magnetic susceptiblility of correlated itinerant fermion systems was so far lacking. Here we study the temperature and doping evolution of these quantities on the two-dimensional Hubbard model using cluster dynamical mean field theory. We recover the suppression of the Knight shift and the linear-in-T spin echo decay that increases with doping. The relaxation rate shows a marked increase as T is lowered but no indication of a pseudogap on the Cu site, and a clear downturn on the O site, consistent with experimental results on single layer materials but different from double layer materials. The consistency of these results with experiment suggests that the pseudogap is well described by strong short-range correlation effects.
In this paper, we try to understand the pseudogap phenomenon observed in the cuprate superconductor through a model study. Specifically, we explore the so-called low-temperature pseudogap state by turning off the superconducting (SC) off diagonal long range order in an ansatz state for the t – J model (Weng 2011 New J. Phys. 13 103039 ). Besides strong non-Gaussian SC fluctuations, the resulting state also exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous 'normal state' properties are found in qualitative consistency with experimental measurements in the cuprates. Such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the SC ground state. A critical comparison with other approaches to the doped Mott insulator is also made.
Using the dynamical cluster approximation and quantum Monte Carlo simulations we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping . In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long-range antiferromagnetic correlations. The physics in the proximity of (0, pi) is dramatically influenced by t' and determined by the short range correlations. The effect t' of on the low-energy angle-resolved photoemission spectroscopy spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility and produce a concomitant gap in the single-particle spectra near (pi, pi/2), but not necessarily at a location in the proximity of the Fermi surface.
The influence of the next-nearest-neighbor (NNN) antiferromagnetic interaction J ’has been examined within t-t'-J-J ’model in an exact technique. An 8-site square cluster is chosen as the representative of the system. The effect of the next-nearest-neighbor (NNN) antiferromagnetic interaction on various ground state properties such as electron-electron correlation, spin-spin correlation, effective hopping amplitude etc. has been studied. Temperature variation of the susceptibility shows that J ’suppresses short range antiferromagnetic order. Applying periodic boundary conditions, the calculations have been extended beyond the 8-site limit.
Long-wavelength spin fluctuations prohibit antiferromagnetic long-range order at finite temperature in two dimensions. Nevertheless, the correlation length starts to grow rapidly at a crossover temperature, leading to critical slowing down and to a renormalized-classical regime over a wide range of temperature, between a fraction of the mean-field transition temperature and the zero-temperature ordered state. This leads to a single-particle pseudogap of the kind observed in electron-doped cuprates. Very few theoretical methods can claim an accurate description of this regime. The challenge is that in this regime Fermi-liquid quasiparticles are already destroyed and new quasiparticles of the ordered state are not fully formed yet. Here, we study this problem for the two-dimensional Hubbard model by first generalizing the two-particle self-consistent approach. Using a special algorithm, spin fluctuations are treated in the thermodynamic limit even for large correlation lengths. The effects of Kanamori-Br\"uckner screening, of classical and of quantum fluctuations are taken into account. Results are presented at half filling for the one-band Hubbard model with nearest-neighbor hopping. They agree well with available benchmark diagrammatic quantum Monte Carlo at high temperature where the pseudogap opens up. In addition to temperature-dependent spectral properties, we find quantum corrections to the zero-temperature renormalized mean-field antiferromagnetic gap. Finally, analytic continuation of the Matsubara results for spectral functions show that the pseudogap opens up at significantly higher temperature than was previously identified based on the Matsubara data only.