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We investigate the center-of-mass momentum distribution $n_{\boldsymbol Q}$of Cooper pairs and their first-order correlation function $g_1(r)$ in astrongly interacting two-dimensional Fermi gas. Recently, the BKT(Berezinskii-Kosterlitz-Thouless) transition was reported in a two-dimensional$^6$Li Fermi gas, based on (1) the observations of anomalous enhancement of$n_{{\boldsymbol Q}={\boldsymbol 0}}$ [M. G. Ries, et. al., Phys. Rev. Lett.114, 230401 (2015)], as well as (2) a power-law behavior of $g_1(r)$ [P. A.Murthy, et. al., Phys. Rev. Lett. 115, 010401 (2015)]. However, includingpairing fluctuations within a $T$-matrix approximation (TMA), we show thatthese results can still be explained as strong-coupling properties of anormal-state two-dimensional Fermi gas. Our results indicate the importance offurther experimental observations, to definitely confirm the realization of theBKT transition in this system. Since the BKT transition has been realized in atwo-dimensional ultracold Bose gas, our results would be useful for theachievement of this quasi-long range order in an ultracold Fermi gas.

physical review. a/physical review, a

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