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arXiv:cond-mat/9405071

Evidence for a Pseudogap Above the Critical Temperature in the Attractive Hubbard Model

José Jesús Rodríguez-Núñez, Sandra Schafroth, R. Micnas, T. Schneider, Beck, H., M. H. Pedersen

Published May 25, 1994• 0 citations
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Abstract

We explore the effect of fluctuations for $T \geq T_c$ in the 2-D negative Hubbard model within the framework of the selfconsistent T-matrix formalism, which goes beyond the BCS approximation and includes pair fluctuations. We enter the regime where correlations are important, namely, $U/t = -4.0$, where $t$ denotes the hopping matrix element between nearest neighboors and $U$ is the strength of the on-site interaction. Our results include: 1) In comparison to the free case, the distribution function, $n({\bf k})$, reveals considerable renormalization. This fact makes us conclude that the Fermi surface is blurred for correlated electron systems; 2) There is a pseudogap in the density of states, $N(ω)$, around the chemical potential, $μ$; and 3) The real part of the T-matrix, at zero frequency and zero momentum, vs $T/t$ shows a divergence at a particular temperature. This last result shows that more approximate T-matrix calculations, extended to $T~=~0$ are meaningless.

DOI
10.48550/arxiv.cond-mat/9405071

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Pair fluctuation effects above TcT_{\rm c}Tc​
We explore the occurrence of pairing effects above TcT_{\rm c}Tc​ in the 2D attractive Hubbard model. The presence of pairs above TcT_{\rm c}Tc​ goes beyond the BCS approximation, in which pair formation and condensation occur at the same temperature. Using the fully self-conserving TTT-matrix formalism, which is valid above TcT_{\rm c}Tc​, we find that (1) the distribution function, n(k)n(k)n(k), shows a 10\% change of the weight from ``below'' to ``above'' kFk_{\rm F}kF​ with respect to the free case, and (2) the phase shift, δϕ(ω,k)δϕ(ω,k)δϕ(ω,k), shows ΘΘΘ-like behavior as a function of ωωω for large momentum kkk along the diagonal of the Brillouin zone. Our calculations have been carried out for an interaction of U/t=−4.0U/t = - 4.0U/t=−4.0 and a temperature of T/t=0.125T/t = 0.125T/t=0.125, where ttt is the hopping matrix element between nearest neighbors. We conclude that for such an interaction value the Fermi surface is not a well-defined quantity.
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The attractive Hubbard model plays a paradigmatic role in the study of superconductivity (superfluidity) and has become directly realizable in ultracold atom experiments on optical lattices. However, the critical temperatures, TcT_cTc​'s, remain lower than the lowest temperatures currently achievable in experiments. Here, we explore a possible route to enhance TcT_cTc​ by introducing an additional next-nearest-neighbor (NNN) hopping, t′t^\primet′, in a two-dimensional square lattice. We perform sign-problem-free determinant quantum Monte Carlo simulations to compute response functions such as pairing correlation functions, superfluid density, and uniform spin susceptibility. Our results show that a judicious choice of t′t^\primet′ can increase TcTcTc by up to 50%50\%50% compared to the case with only nearest-neighbor hopping. In contrast, the preformed pairs temperature scale, named pairing temperature, TpT_pTp​, decreases with increasing ∣t′/t∣|t^{\prime}/t|∣t′/t∣, which should represent a reduction of the pseudogap region, favoring a more BCS-like behavior at intermediate coupling. We further analyze the interacting density of states to characterize the transition from a pseudogap regime to a fully gapped superconducting state. These findings suggest that NNN hopping could be a viable route to increase TcT_cTc​ to values closer to experimentally accessible temperature scales.
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.
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