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arXiv:cond-mat/9808107 · Journal of Physics Condensed Matter

The pseudogap and photoemission spectra in the attractive Hubbard model

P. E. Kornilovitch, Bumsoo Kyung

Published Jan 1, 1999• 0 citations
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Abstract

Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T -matrix equations are solved numerically in the real-time domain. The single-particle spectral function has a two-peak structure resulting from the presence of bound states. The spectral function is suppressed at the chemical potential, leading to a pseudogap-like behaviour. At high temperatures and densities the pseudogap diminishes and finally disappears; these findings are similar to the experimental observations for the cuprates.

DOI
10.1088/0953-8984/11/3/013

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Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T -matrix equations are solved numerically in the real-time domain. The single-particle spectral function has a two-peak structure resulting from the presence of bound states. The spectral function is suppressed at the chemical potential, leading to a pseudogap-like behaviour. At high temperatures and densities the pseudogap diminishes and finally disappears; these findings are similar to the experimental observations for the cuprates.
A model with d-wave pairing symmetry is studied by employing a nonperturbative sum-rule approach. At low temperature the magnitude of a normal-state pseudogap shows strong $\stackrel{\ensuremath{\rightarrow}}{k}$ or angle dependence well fitted by $\mathrm{cos}2\ensuremath{\varphi}$ form. With increasing temperature, the pseudogap closes at some critical angle ${\ensuremath{\varphi}}_{c},$ and beyond this angle a single quasiparticlelike peak appears. The resulting Fermi surface is strongly temperature dependent. Both in the spectral function and the density of states, the pseudogap disappears in a manner that the spectral weight fills in the pseudogap instead of closing it with increasing temperature. All these features are qualitatively consistent with angle resolved photoemission spectroscopy for underdoped cuprates.
A conserving TTT-matrix approximation is applied to the two-dimensional attractive Hubbard model in the low-density regime. A set of self-consistent equations is solved in the real-frequency domain to avoid the analytic continuation procedure. By tuning the chemical potential the particle density was varied in the limits 0.01<n<0.180.01<n<0.180.01<n<0.18. For the value of the attractive potential U=8tU\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8tU=8t the binding energy of pairs monotonically decreases with increasing nnn, from its zero-density limit 2.3t2.3t2.3t, and vanishes at a critical density ncr=0.19{n}_{\mathrm{cr}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.19ncr​=0.19. A pairing-induced pseudogap in the single-particle density of states is found at low densities and temperatures.
In the half-filled one-orbital Hubbard model on a square lattice, we find pseudogap-like features in the form of two-peak structures associated with the momentum-resolved spectral function. These features exist within the temperature window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, where TN{T}_{N}TN​ is the N\'eel temperature and T∗{T}^{*}T∗ is the temperature below which there exists a well-formed dip in the density of state. Inside the window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function grows on moving away from the point ($\ensuremath{\pi}/2,\ensuremath{\pi}/2$) along the normal state Fermi surface toward $(\ensuremath{\pi},0)$, a behavior with remarkable similarities to what is observed in the ddd-wave state and pseudogap phase of high-Tc{T}_{c}Tc​ cuprates. We unveil these features by using a parallelized cluster-based Monte Carlo method for simulating the magnetic order parameter fields on a superlattice. The method enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\ensuremath{\approx}240 \ifmmode\times\else\texttimes\fi{}$ 240 with an almost negligible finite-size effect.
We compute high-resolution angle-resolved photoemission spectroscopy of the Hubbard model using the unbiased determinant quantum Monte Carlo algorithm, revealing an asymmetry between electron and hole doping. Electron doping exhibits more coherent quasiparticles and stronger antiferromagnetic correlations compared to hole doping. At low doping, a nodal-antinodal dichotomy on the Fermi surface is observed, similar to cuprate experiments. The dichotomy reflects the momentum dependence of the Mott gap, as manifested in both the spectral function and the self-energy. For hole doping, we observe a transition towards the pseudogap, without signature of pocket formation. The simulated nuclear magnetic resonance pseudogap temperatures do not necessarily agree with the temperature determined by spectroscopy. These findings collectively suggest the pseudogap is a smooth crossover driven by strong correlations.
We study excitation-spectrum and normal-state properties of the two-dimensional attractive Hubbard model using the conserving, self-consistent T-matrix formalism in the intermediate coupling regime and at low electron concentration. Numerical results are presented for one-particle and two-particle excitation spectra, the one-particle momentum distribution, the chemical potential, and the static spin susceptibility. For a coupling strength of U/t=4.0, the one-particle spectral function, A(k,\ensuremath{\omega}), shows two peaks of different weights. One peak can be associated with pair formation, whereas the other corresponds to renormalized quasiparticle excitation. It turns out that the two-band feature is reasonably well described by an ansatz for A(k,\ensuremath{\omega}), which satisfies the first four frequency moments.
One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak-coupling regime using the non-self-consistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real-frequency axis. For temperatures sufficiently close to the superconducting transition temperature, a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing importance of pair fluctuations.