# Topological Fulde-Ferrell Superfluids in Triangular Lattices

## TL;DR

This paper theoretically explores topological Fulde-Ferrell superfluids in a triangular lattice with spin-orbit coupling and in-plane magnetic field, revealing various topological phases with distinct Chern numbers and chiral edge states.

## Contribution

It introduces a model for topological FF superfluids on a triangular lattice with SOC, identifying multiple topological phases and their edge states, advancing understanding of topological superfluidity.

## Key findings

- Identification of topological FF phases with Chern numbers ±1 and -2.
- Phase boundaries determined by Pfaffian sign change.
- Chiral edge states characterized for different topological phases.

## Abstract

Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) phases were proposed for superconductors or superfluids in strong magnetic field. With the experimental progresses in ultracold atomic systems, topological FFLO phases has also been put forward, since it is a natural consequence of realizable spin-orbital coupling (SOC).In this work, we theoretically investigate a triangular lattice model with SOC and in-plane field. By constructing the phase diagram, we show that it can produce topological FF states with Chern numbers, $C=\pm1$ and $C=-2$. We get the phase boundaries by the change of the sign of Pfaffian. The chiral edge states for different topological FF phases are also elucidated.