Topological Fermi arcs in superfluid 3He

We consider fermionic states bound on domain walls in a Weyl superfluid He-3-A and on interfaces between He-3-A and a fully gapped topological superfluid He-3-B. We demonstrate that in both cases the fermionic spectrum contains Fermi arcs that are continuous nodal lines of energy spectrum terminating at the projections of two Weyl points to the plane of surface states in momentum space. The number of Fermi arcs is determined by the index theorem that relates bulk values of the topological invariant to the number of zero-energy surface states. The index theorem is consistent with an exact spectrum of Bogolubov-de Gennes equation obtained numerically, meanwhile, the quasiclassical approximation fails to reproduce the correct number of zero modes. Thus we demonstrate that topology describes the properties of the exact spectrum beyond the quasiclassical approximation. DOI: 10.1103/PhysRevB.86.214511