Topological superfluids with time reversal symmetry

TL;DR

This paper demonstrates that certain time-reversal invariant superfluids in two and three dimensions possess topological phases, with the B-phase of helium-3 being a non-trivial topological superfluid exhibiting gapless edge states and exotic vortices.

Contribution

It identifies topological invariants in time-reversal invariant superfluids and classifies the B-phase of helium-3 as a non-trivial topological superfluid with unique edge and vortex properties.

Findings

B-phase of helium-3 is a non-trivial topological superfluid.

Non-trivial topological superfluids have gapless edge states.

Vortices in these superfluids can host non-abelian zero modes.

Abstract

It is shown that superfluids in two and three dimensions which have time reversal invariant ground states have phases which are distinguished by a topological invariant. Further, it is shown that the B-phase of $^3$ He is a superfluid in the non-trivial topological class. Superfluids in the non-trivial topological class are shown to have gapless edge states and support various kinds of vortices with zero energy modes localized in their cores. Some of these vortices have non-abelian statistics.