The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition and show that superfluidity is even more sensitive to imbalance than for three-dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allows to identify a phase-separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition and show that superfluidity is even more sensitive to imbalance than for three-dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allows to identify a phase-separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime.
Abstract The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.
We study the superfluid properties of two-dimensional spin-population-imbalanced Fermi gases to explore the interplay between the Berezinskii-Kosterlitz-Thouless (BKT) phase transition and the possible instability towards the Fulde-Ferrell (FF) state. By the mean-field approximation together with quantum fluctuations, we obtain phase diagrams as functions of temperature, chemical potential imbalance, and binding energy. We find that the fluctuations change the mean-field phase diagram significantly. We also address possible effects of the phase separation and/or the anisotropic FF phase to the BKT mechanism. The superfluid density tensor of the FF state is obtained, and its transverse component is found always vanishing. This causes divergent fluctuations and possibly precludes the existence of the FF state at any nonzero temperature.
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 perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wave functions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a nonmonotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.
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.