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

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