Momentum distribution of Cooper-pairs and strong-coupling effects in a two-dimensional Fermi gas near the Berezinskii-Kosterlitz-Thouless transition

TL;DR

This paper analyzes the strong-coupling behavior of a 2D ultracold Fermi gas, showing that pairing fluctuations can explain the increase in zero-momentum Cooper pairs without invoking the BKT transition.

Contribution

It demonstrates that pairing fluctuations account for the observed increase in zero-momentum Cooper pairs, challenging the necessity of the BKT transition assumption in 2D Fermi gases.

Findings

The distribution function of Cooper pairs increases at zero momentum with decreasing temperature.

The observed pairing behavior can be explained without assuming a BKT transition.

Results align with recent experimental data on 2D $^6$Li Fermi gases.

Abstract

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal state. Including pairing fluctuations within the framework of a $T$-matrix approximation, we calculate the distribution function $n({\boldsymbol Q})$ of Cooper pairs in terms of the center of mass momentum ${\boldsymbol Q}$. In the strong-coupling regime, $n({\boldsymbol Q}=0)$ is shown to exhibit a remarkable increase with decreasing the temperature in the low temperature region, which agrees well with the recent experiment on a two-dimensional $^6$Li Fermi gas [M. G. Ries, {\it et. al.}, Phys. Rev. Lett. {\bf 114}, 230401 (2015)]. Our result indicates that the observed remarkable increase of the number of Cooper pairs with zero center of mass momentum can be explained without assuming the Berezinskii-Kosterlitz-Thouless (BKT) transition, when one properly includes pairing fluctuations that are enhanced by the low-dimensionality of the system. Since the BKT transition is a crucial topic in two-dimensional Fermi systems, our results would be useful for the study toward the realization of this quasi-long-range order in an ultracold Fermi gas.