Pseudogaps and phase-fluctuations

Morio Matsumoto, Ryo Hanai, Daisuke Inotani +1 more

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $ρ(ω)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $ρ(ω)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $ρ(ω)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

Albert D. Wheelon

Thomas Maier, Douglas J. Scalapino

Abstract At temperatures above the superconducting transition temperature, the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here, we study the d-wave pairfield susceptibility of a 2D Hubbard model for a doping which has a pseudogap (PG) and for a doping which does not. In both cases, there will be a region of Kosterlitz–Thouless fluctuations as the transition at TKT is approached. Above this region, we find evidence for pairfield-order parameter-phase fluctuations for dopings with a PG and BCS Cooper pair fluctuations for dopings without a PG.

J. D. Fan, Y. M. Malozovsky

Serghei N. Klimin, Jacques Tempere, J. T. Devreese

The physics of the pseudogap state is intimately linked with the pairing mechanism that gives rise to superfluidity in quantum gases and to superconductivity in high- T c cuprates, and therefore, both in quantum gases and in superconductors, the pseudogap state and preformed pairs have been under intensive experimental scrutiny. Here, we develop a path integral treatment that provides a divergence-free description of the paired state in two-dimensional Fermi gases. Within this formalism, we derive the pseudogap temperature and the pair fluctuation spectral function, and compare these results with a recent experimental measurement of the pairing in the two-dimensional Fermi gas. The removal of the infrared divergence in the number equations is shown both numerically and analytically, through a study of the long-wavelength and low-energy limit of the pair fluctuation density. Besides the pseudogap temperature, the pair formation temperature and the critical temperature for superfluidity are also derived. The latter corresponds to the Berezinski–Kosterlitz–Thouless (BKT) temperature. The pseudogap temperature, which coincides with the pair formation temperature in the mean field, is found to be suppressed with respect to the pair formation temperature by fluctuations. This suppression is strongest for large binding energies of the pairs. Finally, we investigate how the pair formation temperature, the pseudogap temperature and the BKT temperature behave as a function of both binding energy and imbalance between the pairing partners in the Fermi gas. This allows us to set up phase diagrams for the two-dimensional Fermi gas, in which the superfluid phase, the phase-fluctuating quasicondensate and the normal state can be identified.