We investigate single-particle excitations and strong-coupling effects in a twodimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states ρ ( ω ) near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T BKT . Near T BKT , we show that superfluid fluctuations induce a pseudogap in ρ (ω). The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a twodimensional 40 K Fermi gas has recently been realized, our results would contribute to the understanding of single-particle properties near the BKT instability.
We investigate single-particle excitations and strong-coupling effects in a twodimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states ρ ( ω ) near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T BKT . Near T BKT , we show that superfluid fluctuations induce a pseudogap in ρ (ω). The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a twodimensional 40 K Fermi gas has recently been realized, our results would contribute to the understanding of single-particle properties near the BKT instability.
We theoretically investigate strong-coupling properties of a two-dimensional Fermi gas in the normal phase. Including pairing fluctuations within the framework of a self-consistent T -matrix approximation, we calculate the single-particle density of states (DOS) near the observed Berezinskii-Kosterlitz-Thouless phase transition temperature T BKT . We show that the pseudogap phenomenon associated with strong pairing fluctuations appears as an almost fully gapped single-particle density of states in the strong-coupling regime, indicating that amplitude fluctuations of the order parameter are almost absent and the system is dominated by phase fluctuations of the order parameter, as expected in a two-dimensional system near T BKT . On the other hand, although pairing fluctuations are enhanced by the low-dimensionality of the system, they are found to be still not strong enough to open such a full gap in the intermediate coupling (crossover) regime. In this regime, a dip structure is only seen in DOS around ω = 0, indicating that amplitude of the superfluid order parameter is also fluctuating, in addition to phase fluctuations. In theoretically determining T BKT in a two-dimensional Fermi gas, it is frequently assumed that, while phase fluctuations exist, the amplitude of the superfluid order parameter is fixed. However, our results indicate the necessity of including both amplitude and phase fluctuations of the order parameter in evaluating T BKT in the crossover region. Since the BKT phase transition has recently been reported in a two-dimensional 6 Li Fermi gas, our results would be useful for the theoretical study of this observed novel Fermi superfluid and effects of strong low-dimensional pairing fluctuations.
This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii-Kosterlitz-Thouless (BKT) temperature TBKT as a function of \emph{attractive} pairing strength by associating it with the onset of quasi-condensation in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established Quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS-BEC crossover theory for fermions, leads to non-monotonic behavior for TBKT as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that TBKT has an absolute maximum of the order of 0.1EF. We discuss how our results compare with those derived from the Nelson Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in TBKT followed by an often dramatic decrease before the system enters the BEC regime.
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 TBKTexp in a 6Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in ρ(ω) at TBKTexp still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed TBKTexp 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.
Abstract This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii–Kosterlitz–Thouless (BKT) temperature T BKT as a function of attractive pairing strength by associating it with the onset of ‘quasi-condensation’ in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS–BEC crossover theory for fermions, leads to non-monotonic behavior for T BKT as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that T BKT has an absolute maximum of the order of 0.1E F. We discuss how our results compare with those derived from the Nelson–Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in T BKT followed by an often dramatic decrease before the system enters the BEC regime.
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions offdiagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart.Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime.The theory is also compared with experimental data.Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.
We investigate the center-of-mass momentum distribution ${n}_{\mathbit{Q}}$ of Cooper pairs and their first-order correlation function g1(r) in a strongly interacting two-dimensional Fermi gas. Recently, the Berezinskii-Kosterlitz-Thouless (BKT) transition was reported in a two-dimensional 6Li Fermi gas, based on (1) the observations of anomalous enhancement of ${n}_{\mathbit{Q}=\mathbit{0}}$ [Ries et al., Phys. Rev. Lett. 114, 230401 (2015)] , as well as (2) a power-law behavior of g1(r) [Murthy et al., Phys. Rev. Lett. 115, 010401 (2015)]. However, including pairing fluctuations within a T-matrix approximation (TMA), we show that these results can still be explained as strong-coupling properties of a normal-state two-dimensional Fermi gas. Our results indicate the importance of further experimental observations, to definitely confirm the realization of the BKT transition in this system. Since the BKT transition has been realized in a two-dimensional ultracold Bose gas, our results would be useful for the achievement of this quasi-long-range order in an ultracold Fermi gas.