  Topological superfluids usually refer to a superfluid state which is gapped
in the bulk but metallic at the boundary. Here we report that a gapless,
topologically non-trivial superfluid with inhomogeneous Fulde-Ferrell pairing
order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas,
in the presence of both in-plane and out-of-plane Zeeman fields. The
Fulde-Ferrell pairing - induced by the spin-orbit coupling and in-plane Zeeman
field - is responsible for this gapless feature. This exotic superfluid has a
significant Berezinskii-Kosterlitz-Thouless (BKT) transition temperature and
has robust Majorana edge modes against disorder owing to its topological
nature.
