Nodal line topological superfluid and multiply protected Majorana Fermi arc in a three-dimensional...

We theoretically study a time-reversal-invariant three-dimensional superfluid model by stacking in z direction identical bilayer models with intralayer spin-orbit coupling and contrary Zeeman energy splitting for different layers, which has been suggested recently to realize two-dimensional time-reversal-invariant topological superfluid. We find that this model shows two kinds of topologically nontrivial phases: gapless phases with nodal lines in pairs protected by chiral symmetry and a gapped phase, both of which support a time-reversal-invariant Majorana Fermi arc (MFA) on the yz and xz side surface. These MFA abide by time-reversal and particle-hole symmetries and are topologically protected by the winding numbers in mirror subspaces and the Z ₂ numbers of two-dimensional DIII class topological superfluid, which are different from MFA in the time-reversal broken Weyl superfluid protected by nonzero Chern numbers. This important observation means that MFA in our model represents a new type of topological state not explored previously. The Zeeman field configuration in our model is relevant to the antiferromagnetic topological insulator MnBi₂Te₄, thus our work stimulates the further studies on superconducting effects in the realistic antiferromagnetic topological insulator.