Topological Fulde-Ferrell-Larkin-Ovchinnikov states in spin-orbit-coupled Fermi gases

Pairing in an attractively interacting two-component Fermi gas in the absence of time-reversal symmetry or inversion symmetry may give rise to exotic superfluid states. Notable examples range from the Fulde-Ferrell-Larkin-Ovchinnikov state with a finite centre-of-mass momentum in a polarized Fermi gas to the topological superfluid (TSF) state in a two-dimensional (2D) Fermi gas under Rashba spin-orbit coupling and an out-of-plane Zeeman field. Here we show that a TSF state with a single-component nonzero centre-of-mass momentum, called a topological Fulde-Ferrell (tFF) state, can be stabilized in a 2D Fermi gas with Rashba spin-orbit coupling and both in-plane and out-of-plane Zeeman fields. The tFF state features a non-trivial Berry phase, along with unique properties that may be detected using existing experimental techniques.