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Pairing in an attractively interacting two-component Fermi gas in the absenceof the inversion symmetry and/or the time-reversal symmetry may give rise toexotic superfluid states. Notable examples range from theFulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with a finite center-of-massmomentum in a polarized Fermi gas, to the topological superfluid state in atwo-dimensional Fermi gas under Rashba spin-orbit coupling and an out-of-planeZeeman field. Here, we show that a topological FFLO state can be stabilized ina two-dimensional Fermi gas with Rashba spin-orbit coupling and both in-planeand out-of-plane Zeeman fields. We characterize the topological FFLO state by anon-trivial Berry phase, and demonstrate the stability region of the state onthe zero-temperature phase diagram. Given its unique properties in both thequasi-particle dispersion spectra and the momentum distribution, signatures ofthe topological FFLO state can be detected using existing experimentaltechniques.

Topological Fulde-Ferrel-Larkin-Ovchinnikov states in Spin-orbit Coupled Fermi Gases