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Weyl fermions, first proposed for describing massless chiral Dirac fermionsin particle physics, have not been observed yet in experiments. Recently, mucheffort has been devoted to explore Weyl fermions around band touching points ofsingle particle energy dispersions in certain solid state materials (named\textit{Weyl semimetals}), similar as graphene for Dirac fermions. Here we showthat such Weyl semimetals also exist in the quasiparticle excitation spectrumof a three-dimensional (3D) spin-orbit coupled Fulde-Ferrell (FF) superfluid.By varying Zeeman fields, the properties of Weyl fermions, such as theircreation and annihilation, number and position, as well as anisotropic lineardispersions around band touching points, can be tuned. We study themanifestation of anisotropic Weyl fermions in sound speeds of FF fermionicsuperfluids, which are detectable in experiments.

Anisotropic Weyl Fermions from Quasiparticle Excitation Spectrum of a 3D Fulde-Ferrell Superfluid