Nodal line topological superfluid and multiply protected Majorana Fermi arc in a three-dimensional time-reversal-invariant superfluid model

Abstract

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 Z2 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.