Topological Fermi arcs in superfluid $^3$He

TL;DR

This paper investigates fermionic states on domain walls in superfluid $^3$He, revealing Fermi arcs linked to topological invariants, and highlights the importance of exact solutions over quasiclassical approximations.

Contribution

It demonstrates the existence of Fermi arcs in superfluid $^3$He and establishes the topological index theorem's role in determining their number, surpassing quasiclassical methods.

Findings

Fermi arcs are present in superfluid $^3$He-A and at interfaces with $^3$He-B.

The number of Fermi arcs is dictated by a topological index theorem.

Exact solutions confirm the index theorem, while quasiclassical approximation fails to do so.

Abstract

We consider fermionic states bound on domain walls in a Weyl superfluid $^3$He-A and on interfaces between $^3$He-A and a fully gapped topological superfluid $^3$He-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.