  We study the superfluid properties of two-dimensional
spin-population-imbalanced Fermi gases to explore the interplay between the
Berezinskii-Kosterlitz-Thouless (BKT) phase transition and the possible
instability towards the Fulde-Ferrell (FF) state. By the mean-field
approximation together with quantum fluctuations, we obtain phase diagrams as
functions of temperature, chemical potential imbalance and binding energy. We
find that the fluctuations change the mean-field phase diagram significantly.
We also address possible effects of the phase separation and/or the anisotropic
FF phase to the BKT mechanism. The superfluid density tensor of the FF state is
obtained, and its transverse component is found always vanishing. This causes
divergent fluctuations and possibly precludes the existence of the FF state at
any non-zero temperature.
