Cooper pairs with zero center-of-mass momentum and their first-order correlation function in a two-dimensional ultracold Fermi gas near a Berezinskii-Kosterlitz-Thouless transition

We investigate the center-of-mass momentum distribution n(Q) of Cooper pairs and their first-order correlation function g(1)(r) in a strongly interacting two-dimensional Fermi gas. Recently, the Berezinskii-Kosterlitz-Thouless (BKT) transition was reported in a two-dimensional Li-6 Fermi gas, based on (1) the observations of anomalous enhancement of n(Q=0) [Ries et al., Phys. Rev. Lett. 114, 230401 (2015)], as well as (2) a power-law behavior of g(1)(r) [Murthy et al., Phys. Rev. Lett. 115, 010401 (2015)]. However, including pairing fluctuations within a T-matrix approximation (TMA), we show that these results can still be explained as strong-coupling properties of a normal-state two-dimensional Fermi gas. Our results indicate the importance of further experimental observations, to definitely confirm the realization of the BKT transition in this system. Since the BKT transition has been realized in a two-dimensional ultracold Bose gas, our results would be useful for the achievement of this quasi-long-range order in an ultracold Fermi gas.