Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids

TL;DR

This paper investigates how quantum and thermal fluctuations affect superfluid properties in two-dimensional Fermi gases, revealing significant deviations from mean-field predictions and aligning well with recent experimental results.

Contribution

The study introduces a one-loop Gaussian fluctuation approach to accurately describe superfluid properties in 2D Fermi gases, highlighting the importance of fluctuations beyond mean-field theory.

Findings

Renormalization of first and second sound velocities due to fluctuations

Significant deviation of critical temperature from mean-field estimates

Good agreement with recent experimental measurements of BKT transition and sound velocities

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 quasi-condensation and algebraic long-range order to a normal phase, where 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 novel predictions for the second sound as a function of interaction strength and temperature, open for experimental verification.