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arXiv:nucl-th/9902038 · Physical Review Letters

Precritical Pair Fluctuations and Formation of a Pseudogap in Low-Density Nuclear Matter

Alexander Schnell, GERD RÖPKE, Peter Schuck

Published Sep 6, 1999• 37 citations
arXivHTMLPDF

Abstract

Low-density nuclear matter at finite temperature is considered representing the strong coupling situation of a highly correlated fermion system. One-particle self-energies and the density of states in the vicinity of the pairing transition point are presented. Within the Green function approach, model calculations are performed using the thermodynamic $T$ matrix in ladder approximation. As a main result the formation of a pseudogap in the level density near the critical temperature of the pairing phase transition has been found. It is shown that compared to mean-field approaches the scenario of the onset of the pairing transition is essentially changed if correlations are taken into account.

DOI
10.1103/physrevlett.83.1926

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Low-density nuclear matter at finite temperature is considered representing the strong coupling situation of a highly correlated fermion system. One-particle self-energies and the density of states in the vicinity of the pairing transition point are presented. Within the Green function approach, model calculations are performed using the thermodynamic TTT matrix in ladder approximation. As a main result the formation of a pseudogap in the level density near the critical temperature of the pairing phase transition has been found. It is shown that compared to mean-field approaches the scenario of the onset of the pairing transition is essentially changed if correlations are taken into account.
The pseudogap is a ubiquitous phenomenon in strongly correlated systems, such as high-T c superconductors, ultracold atoms, and nuclear physics.Whereas pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental one-dimensional models, that is, Gaudin-Yang model.In this paper, we show how the pseudogap effect emerges in the single-particle excitation in this system using a diagrammatic approach.Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to the pseudogap state with increasing the attractive interaction and the number density at finite temperature.Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, indicating the validity of our approach even in the region where the pseudogap appears.
The origin of the pseudogap behavior, found in many high-TcT_cTc​ superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a gap-filling rather than gap-closing behavior, consistent with experimental observations. Our results provide the first unambiguous lattice model realization of a pseudogap state in a strongly correlated system, driven by superconducting fluctuations.
We consider the layered attractive Hubbard model with a moderate interaction strength at quarter filling. The Green's function, self-energy, and density of states are calculated for relatively large clusters using the fluctuating local field method within the approximation of vanishing effective interaction. The emergence of a pseudogap is demonstrated for the cluster system, and it is shown that integration over the fluctuating field is equivalent to the summation of zero-mode ladder diagrams above critical temperature. For the large layered system, a pseudogap in the density of states is obtained within a cluster scheme that treats the coupling between layers as a static U(1)U(1)U(1) symmetry-breaking field.
On the basis of an electronic model with separable attractive interaction, the precursors at high temperature and strong coupling of the d-wave superconducting state are investigated in the one-particle spectral function $A(\mathbf{k},\ensuremath{\omega})$ and the total density of states $\ensuremath{\rho}(\ensuremath{\omega}),$ with the use of the self-consistent t-matrix approximation. In the low-density region, it is found that a gaplike structure at the Fermi level appears in $A(\mathbf{k},\ensuremath{\omega})$ and $\ensuremath{\rho}(\ensuremath{\omega})$ above the superconducting transition temperature. It is shown that the pseudogap energy scale is determined by the binding energy of the Cooper pair.
We investigate fluctuation effects in a single-component ultracold Fermi gas with a p-wave interaction. Within the framework of a strong-coupling T-matrix theory, we calculate the single-particle density of states (DOS) at the superfluid phase transition temperature Tc. Starting from the weak-coupling regime, we show that the so-called pseudogap structure develops in DOS, with increasing the strength of a pairing interaction. However, in contrast to the case of s-wave interaction (where the pseudogap size in DOS monotonically increases with increasing the interaction strength), the pseudogap structure is found to gradually disappear in the strong-coupling regime. We point out that this non-monotonic behavior of pseudogap originates from the momentum dependence of p-wave interaction. Our results clarify how the symmetry of pairing interaction affects pseudogap phenomena in strongly correlated fermion systems.
Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( $\ensuremath{\alpha}$-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.