Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover

TL;DR

This paper develops a theoretical framework for the superfluid density in a 2D ultracold atomic gas across the BCS-BEC crossover, accurately predicting the BKT transition temperature and highlighting differences from traditional criteria.

Contribution

It introduces a beyond-mean-field theory including Gaussian fluctuations and analyzes vortex effects to determine the BKT transition in 2D Fermi gases.

Findings

Good agreement with experimental data at zero temperature.

Renormalized superfluid density drops at the BKT transition.

Nelson-Kosterlitz criterion overestimates the BKT temperature.

Abstract

We analyze the theoretical derivation of the beyond-mean-field equation of state for a two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. We show that at zero temperature our theory -- considering Gaussian fluctuations on top of the mean-field equation of state -- is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex-antivortex pairs. By doing so, we determine the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature -- at which the renormalized superfluid density jumps to zero -- as a function of the inter-atomic potential strength. We find that the Nelson-Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover.