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Physical Review Letters

Pairing and spin gap in the normal state of short coherence length superconductors

Mohit Randeria, Nandini Trivedi, Adriana Moreo, Richard T. Scalettar

Published Sep 28, 1992• 348 citations
Publisher

Abstract

We study the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. We show that singlet pairing correlations develop above ${\mathit{T}}_{\mathit{c}}$, 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/${\mathit{T}}_{1}$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-${\mathit{T}}_{\mathit{c}}$ systems.

DOI
10.1103/physrevlett.69.2001

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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 \ensuremathχs{\mathrm{\ensuremath{\chi}}}_{\mathit{s}}\ensuremathχs​ 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 \ensuremathχs{\mathrm{\ensuremath{\chi}}}_{\mathit{s}}\ensuremathχs​. This provides a simple, qualitative explanation for the spin-gap behavior observed in several high-Tc{\mathit{T}}_{\mathit{c}}Tc​ systems.
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 ${\ensuremath{\chi}}_{s}$ and the low frequency spin spectral weight track N(0)N\left(0\right)N(0), 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 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.
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 study the thermodynamics of a superconductor with strongly bound Cooper pairs by solving the self-consistent T-matrix equations for the attractive Hubbard model within a local approximation. We determine the transition temperature as a function of the interaction strength at quarter filling, and compute the temperature dependence of the superconducting order parameter, the specific heat, the spin susceptibility, and the density of local pairs in the normal and superconducting phase. Pronounced deviations from BCS behavior are found already for moderate interactions, where superconductivity sets in at a critical temperature above the coherence temperature for Fermi liquid behavior.
We study the phase diagram for the attractive (i.e., negative-U) Hubbard model on a simple-cubic lattice, through Monte Carlo simulations. We obtain the critical temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ for superconductivity from a finite-size scaling analysis of the data for the pairing correlations. For fixed on-site attraction U, Tc{\mathit{T}}_{\mathit{c}}Tc​ displays a maximum near the filling factor 0.9, roughly independent of U. For fixed filling we estimate the crossover temperature ${\mathit{T}}^{\ifmmode\times\else\texttimes\fi{}}$(U), separating the normal states: metallic and spin gap. There is also a critical value Up{\mathit{U}}_{\mathit{p}}Up​ for pair formation, the magnitude of which seems to be independent of doping. The relevance of these results to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ oxides is discussed.
We study the phase diagram for the attractive ({\it i.e.,} negative-UUU) Hubbard model on a simple cubic lattice, through Monte Carlo simulations. We obtain the critical temperature, TcT_cTc​, for superconductivity from a finite-size scaling analysis of the data for the pairing correlations. For fixed on-site attraction, UUU, TcT_cTc​ displays a maximum near the filling factor 0.9, roughly independent of UUU. For fixed filling we estimate the crossover temperature T×(U)T^\times(U)T×(U), separating the normal states: metallic and spin-gap. There is also a critical value UpU_pUp​ for pair formation, the magnitude of which seems to be independent of doping. The relevance of these results to the high-TcT_cTc​ oxides is discussed.