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arXiv:cond-mat/9411121 · Physical Review Letters

Deviations from Fermi-Liquid Behavior above Tc in 2D Short Coherence Length Superconductors

Nandini Trivedi, Mohit Randeria

Published Jul 10, 1995• 215 citations
arXivHTMLPDF

Abstract

We show that there are qualitative differences between the temperature dependence of the spin and charge correlations in the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. The one-particle density of states shows a pseudogap above ${T}_{c}$ with a depleted $N\left(0\right)$ with decreasing $T$. The susceptibility ${\ensuremath{\chi}}_{s}$ and the low frequency spin spectral weight track $N\left(0\right)$, which explains the spin-gap scaling: ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}_{s}\left(T\right)$. However, collective excitations contribute to the charge channel, and the compressibility $dn/d\ensuremath{\mu}$ is $T$ independent. This anomalous ``spin-charge separation'' is shown to exist even at intermediate $|U|$ where the momentum distribution $n\left(\mathbf{k}\right)$ gives evidence for a degenerate Fermi system.

DOI
10.1103/physrevlett.75.312

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We show that there are qualitative differences between the temperature dependence of the spin and charge correlations in the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. The one-particle density of states shows a pseudogap above Tc{T}_{c}Tc​ with a depleted N(0)N\left(0\right)N(0) with decreasing TTT. The susceptibility \ensuremathχs{\ensuremath{\chi}}_{s}\ensuremathχs​ and the low frequency spin spectral weight track N(0)N\left(0\right)N(0), which explains the spin-gap scaling: 1/T1T\ensuremath∼\ensuremathχs(T){1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}_{s}\left(T\right)1/T1​T\ensuremath∼\ensuremathχs​(T). However, collective excitations contribute to the charge channel, and the compressibility dn/d\ensuremathμdn/d\ensuremath{\mu}dn/d\ensuremathμ is TTT independent. This anomalous ``spin-charge separation'' is shown to exist even at intermediate ∣U∣|U|∣U∣ where the momentum distribution n(k)n\left(\mathbf{k}\right)n(k) gives evidence for a degenerate Fermi system.
We study the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. We show that singlet pairing correlations develop above Tc{\mathit{T}}_{\mathit{c}}Tc​, and the normal state of a short coherence length superconductor deviates from a canonical Fermi liquid. In the intermediate U regime, the spin susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{s}}$ is strongly temperature dependent, and the low-frequency spectral weight, as measured by the NMR relaxation rate 1/T1{\mathit{T}}_{1}T1​T, is shown to track ${\mathrm{\ensuremath{\chi}}}_{\mathit{s}}$. This provides a simple, qualitative explanation for the spin-gap behavior observed in several high-Tc{\mathit{T}}_{\mathit{c}}Tc​ systems.
The two-dimensional attractive Hubbard model is studied in the weak-to-intermediate-coupling regime by employing a nonperturbative approach. It is shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T∗,{T}^{*},T∗, also in good agreement with quantum Monte Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classical regime $(\ensuremath{\Elzxh}\ensuremath{\omega}<{k}_{B}T)$ of the two-dimensional system. With increasing temperature the spectral weight fills in the pseudogap instead of closing it, and the pseudogap appears earlier in the density of states than in the spectral function. Small temperature changes around T∗{T}^{*}T∗ can modify the spectral weight over frequency scales much larger than temperature. Several qualitative results for the s-wave case should remain true for d-wave superconductors.
We have studied in terms of the effective T-matrix the self-energy part for both the attractive (U<0) and repulsive (U>0) Hubbard models. It is shown that the fluctuation pairing for strong coupling at T>T c for the attractive Hubbard model does not cause any pseudogap behavior in the single-particle density of states. We have also identified the origin of the false pseudogap for that case. Meanwhile, the fluctuation pairing significantly affect the density–density and the current–current correlation functions. As a result, there exists a pseudogap in the charge (and current) response for the attractive Hubbard model. In contrast, the pseudogap in the spin response appears to exist for the repulsive Hubbard model only. It is also shown that the contribution from the Hartree–"Cooper" channel gives an anomalous Fermi liquid term, Im χ c ≈-ω/T, to the charge response of the nearly antiferromagnetic Fermi liquid.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the (±π,0)(\pm π,0)(±π,0), (0,±π)(0,\pm π)(0,±π) regions as the normal state pseudogap observed in the high-TcT_cTc​ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around Q=(π,π){\bf Q}=(π,π)Q=(π,π) and the flatness of the band dispersion around the saddle point.
In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual "pseudogap" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multipoint correlation functions up to fifth order, we uncover a universal scaling behavior in magnetic and higher-order spin-charge correlations characterized by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature [Formula: see text]. Our quantitative findings reveal a qualitative behavior of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way toward the exploration of charge pairing and collective phenomena expected at lower temperatures.
We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering qqq-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.