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We theoretically investigate the superfluid density andBerezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashbaspin-orbit coupled atomic Fermi gas with both in-plane and out-of-plane Zeemanfields. It was recently predicted that, by tuning the two Zeeman fields, thesystem may exhibit different exotic Fulde-Ferrell (FF) superfluid phases,including the gapped FF, gapless FF, gapless topological FF and gappedtopological FF states. Due to the FF paring, we show that the superfluiddensity (tensor) of the system becomes anisotropic. When an in-plane Zeemanfield is applied along the \textit{x}-direction, the tensor component along the\textit{y}-direction $n_{s,yy}$ is generally larger than $n_{s,xx}$ in mostparameter space. At zero temperature, there is always a discontinuity jump in$n_{s,xx}$ as the system evolves from a gapped FF into a gapless FF state. Withincreasing temperature, such a jump is gradually washed out. The critical BKTtemperature has been calculated as functions of the spin-orbit couplingstrength, interatomic interaction strength, in-plane and out-of-plane Zeemanfields. We predict that the novel FF superfluid phases have a significantcritical BKT temperature, typically at the order of $0.1T_{F}$, where $T_{F}$is the Fermi degenerate temperature. Therefore, their observation is within thereach of current experimental techniques in cold-atom laboratories.

Superfluid density and Berezinskii-Kosterlitz-Thouless transition of a spin-orbit coupled Fulde-Ferrell superfluid