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We theoretically study a time-reversal-invariant three-dimensional superfluidmodel by stacking in $z$ direction identical bilayer models with intralayerspin-orbit coupling and contrary Zeeman energy splitting for different layer,which has been suggested recently to realize two-dimensionaltime-reversal-invariant topological superfluid. We find that this model showstwo kinds of topologically nontrivial phases: gapless phases with nodal linesin pairs protected by chiral symmetry and a gapped phase, both of which supporttime-reversal-invariant Majorana Fermi arc (MFA) on the $yz$ and $xz$ sidesurface. These MFA abide by time-reversal and particle-hole symmetries and aretopologically protected by the winding numbers in mirror subspaces and $Z_2$numbers of two-dimensional DIII class topological superfluid, different fromMFA in the time-reversal broken Weyl superfluid protected by nonzero Chernnumber. This important observation means that MFA in our model represents a newtype of topological state not explored previously. The Zeeman fieldconfiguration in our model is relevant to antiferromagnetic topologicalinsulator MnBi$_2$Te$_4$, thus our work stimulates the further studies onsuperconducting effects in the realistic antiferromagnetic topologicalinsulator.

Nodal Line Topological Superfluid and Multiply Protected Majorana Fermi Arc in a Three-Dimensional Time-Reversal-Invariant Superfluid Model