Topological superfluids with time reversal symmetry

TL;DR

The paper demonstrates that time-reversal-invariant superfluids in 2D and 3D are classified by a $Z_2$ topological invariant, with the 3D case tied to the 2D invariant on TR-invariant planes. Using a mean-field BdG framework and patch constructions, it shows robust edge or surface Majorana modes and the existence of exotic vortices carrying zero-energy Majorana states that obey non-Abelian statistics. The B-phase of $^3$He is presented as a concrete nontrivial example, with edge states and 2D Dirac-like surface spectra arising from the bulk topology. These findings illuminate potential platforms for topological quantum computation and guide experimental exploration of TR-invariant topological superfluids.

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.