Spin-orbit-coupling-induced Fulde-Ferrell-Larkin-Ovchinnikov-like Cooper pairing and skyrmion-like polarization textures in optical lattices

We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.