Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) phases were proposed for superconductors or superfluids in a strong magnetic field. With the experimental progress in ultracold atomic systems, topological FFLO phases have also been put forward since it is a natural consequence of realizable spin-orbital coupling (SOC). In this paper, we theoretically investigate a triangular lattice model with SOC and an in-plane field. By constructing the phase diagram, we show that it produces gapped and gapless topological FF phases with Chern numbers $C=\pm 1,\pm 2,-3$, and $-4$. We get the phase boundaries by the change in the sign of the Pfaffian. The chiral edge states for different topological FF phases also are elucidated.

• Received 18 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.063610