We consider fermionic states bound on domain walls in a Weyl superfluid 3He-A and on interfaces between 3He-A and a fully gapped topological superfluid 3He-B. We demonstrate that in both cases fermionic spectrum contains Fermi arcs which 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 which relates bulk values of 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 exact spectrum beyond quasiclassical approximation.
@article{arxiv.1209.3368,
title = {Topological Fermi arcs in superfluid $^3$He},
author = {M. A. Silaev and G. E. Volovik},
journal= {arXiv preprint arXiv:1209.3368},
year = {2013}
}