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 (Formula presented.) of Cooper pairs in terms of the center of mass momentum (Formula presented.). In the strong-coupling regime, (Formula presented.) 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 (Formula presented.) Li Fermi gas (Ries et al. in Phys Rev Lett 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.
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