Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids

Abstract

In two-dimensional systems with a continuous symmetry, the Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless critical temperature marks the transition from a superfluid phase characterized by quasicondensation and algebraic long-range order, to a normal phase in which vortex proliferation completely destroys superfluidity. As opposed to conventional off-diagonal long-range order typical of three-dimensional superfluid systems, algebraic long-range order is driven by quantum and thermal fluctuations strongly enhanced in reduced dimensionality. Motivated by this unique scenario and by the very recent experimental realization of trapped quasi-two-dimensional fermionic clouds, we include one-loop Gaussian fluctuations in the theoretical description of resonant Fermi superfluids in two dimensions demonstrating that first sound, second sound, and also critical temperature are strongly renormalized, away from their mean-field values. In particular, we prove that in the intermediate-and strong-coupling regimes, these quantities are radically different when Gaussian fluctuations are taken into account. Our one-loop theory shows good agreement with very recent experimental data on the Berezinskii-Kosterlitz-Thouless critical temperature [Phys. Rev. Lett. 115, 010401 ( 2015)] and on the first sound velocity, giving predictions for the second sound as a function of interaction strength and temperature that are open for experimental verification

Superfluid density and critical velocity near the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional strongly interacting Fermi gas

“…4(b). Our result shows a significant improvement on the BCS side over the previous theoretical predictions [16,45]. While on the BEC side (i.e., ε B > 0.5ε F ), our result follows closely to the approximate prediction from Landau's formula, since in the latter, the superfluid fraction at low temperatures T ∼ 0.1T F is reasonably approximated.…”

“…While on the BEC side (i.e., ε B > 0.5ε F ), our result follows closely to the approximate prediction from Landau's formula, since in the latter, the superfluid fraction at low temperatures T ∼ 0.1T F is reasonably approximated. In the deep BEC regime our GPF result approaches the anticipated BKT critical temperature of a weakly interacting Bose gas [45,55], since, the molecular scattering length is correctly reproduced in the GPF theory [43,56]. In this respect, the phase diagram Fig.…”

“…4(a) by solid circles, contrasted with the mean-field result (dot-dashed line). The superfluid density of a 2D interacting Fermi gas has been recently calculated by Bighin and Salasnich [45] using Landau's phenomenological formulation for the normal density and the quasiparticle spectrum based on the zerotemperature GPF equation of state [54]. Their result is plotted in Fig.…”

“…For an interacting 2D Fermi gas at zero temperature the problem may be solved by utilizing an additional function which has no singularities or zeros in the left hand-plane [43,49]. At finite temperature, however, the GPF has only been approximately treated by taking into account the effects of low-energy phonon modes [39,45]. Here, we overcome the divergence by writing [53],…”

Kosterlitz-Thouless transition and vortex-antivortex lattice melting in two-dimensional Fermi gases with p - or d -wave pairing

“…At T = 0 we have n = n 0 and therefore the quantum fluctuations [54][55][56] are not taken into account in the present theory. For s-wave pairing, it was found that inclusion of quantum fluctuations leads to slight correction to the KT transition [57,58]. Thus we expect that the present theory can provides reliable results for the KT and VAL transition for higher partial wave pairings.…”