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We study the superfluid properties of two-dimensionalspin-population-imbalanced Fermi gases to explore the interplay between theBerezinskii-Kosterlitz-Thouless (BKT) phase transition and the possibleinstability towards the Fulde-Ferrell (FF) state. By the mean-fieldapproximation together with quantum fluctuations, we obtain phase diagrams asfunctions of temperature, chemical potential imbalance and binding energy. Wefind that the fluctuations change the mean-field phase diagram significantly.We also address possible effects of the phase separation and/or the anisotropicFF phase to the BKT mechanism. The superfluid density tensor of the FF state isobtained, and its transverse component is found always vanishing. This causesdivergent fluctuations and possibly precludes the existence of the FF state atany non-zero temperature.

Fulde-Ferrell states and Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional imbalanced Fermi gases