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We theoretically investigate a three-dimensional Fermi gas with Rashbaspin-orbit coupling in the presence of both out-of-plane and in-plane Zeemanfields. We show that, driven by a sufficiently large Zeeman field, eitherout-of-plane or in-plane, the superfluid phase of this system exhibits a numberof interesting features, including inhomogeneous Fulde-Ferrell pairing, gappedor gapless topological order and exotic quasi-particle excitations known asWeyl fermions that have linear energy dispersions in momentum space (i.e.,massless Dirac fermions). The topological superfluid phase can have either fouror two topologically protected Weyl nodes. We present the phase diagrams atboth zero and finite temperatures and discuss the possibility of theirobservation in an atomic Fermi gas with synthetic spin-orbit coupling. In thiscontext, topological superfluid phases with an imperfect Rashba spin-orbitcoupling are also studied.

Three-dimensional spin-orbit coupled Fermi gases: Fulde-Ferrell pairing, Majorana fermions, Weyl fermions and gapless topological superfluidity