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We study the superfluid weight $D^s$ and Berezinskii-Kosterlitz-Thouless(BKT) transition temperatures $T_{BKT}$ in case of exotic Fulde-Ferrell (FF)superfluid states in lattice systems. We consider spin-imbalanced systems withand without spin-orbit coupling (SOC) accompanied with in-plane Zeeman field.By applying mean-field theory, we derive general equations for $D^s$ and$T_{BKT}$ in the presence of SOC and the Zeeman fields for 2D Fermi-Hubbardlattice models, and apply our results to a 2D square lattice. We show thatconventional spin-imbalanced FF states without SOC can be observed at finitetemperatures and that FF phases are further stabilized against thermalfluctuations by introducing SOC. We also propose how topologically non-trivialSOC-induced FF phases could be identified experimentally by studying the totaldensity profiles. Furthermore, the relative behavior of transverse andlongitudinal superfluid weight components and the role of the geometricsuperfluid contribution are discussed.

Superfluid weight and Berezinskii-Kosterlitz-Thouless temperature of spin-imbalanced and spin-orbit-coupled Fulde-Ferrell phases in lattice systems