  Topological superfluids are recently discovered quantum matters that host
topologically protected gapless edge states known as Majorana fermions - exotic
quantum particles that act as their own anti-particles and obey non-Abelian
statistics. Their realizations are believed to lie at the heart of future
technologies such as fault-tolerant quantum computation. To date, the most
efficient scheme to create topological superfluids and Majorana fermions is
based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit
coupling on the }\textbf{\textit{x-y}}\textbf{ plane and a large out-of-plane
(perpendicular) Zeeman field along the }\textbf{\textit{z}}\textbf{-direction.
Here we propose an alternative setup, where the topological superfluid phase is
driven by applying an in-plane Zeeman field. This scheme offers a number of new
features, notably Cooper pairings at finite centre-of-mass momentum (i.e.,
Fulde-Ferrell pairing) and gapless excitations in the bulk. As a result, a
novel gapless topological quantum matter with inhomogeneous pairing order
parameter appears. It features unidirected Majorana surface states at
boundaries, which propagate in the same direction and connect two Weyl nodes in
the bulk. We demonstrate the emergence of such an exotic topological matter and
the associated Majorana fermions in spin-orbit coupled atomic Fermi gases and
determine its parameter space. The implementation of our scheme in
semiconductor/superconductor heterostructures is briefly discussed.
