Symmetry Protected Topological Superfluid $^3$He-B

Understand

Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid $^3$He has offered a prototypical system to study intertwining of topology and symmetry.

• This article reviews recent progress in understanding the topological superfluidity of $^3$He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory.
• Special focus is placed on the symmetry protected topological superfuidity of the $^3$He-B confined in a slab geometry.
• The $^3$He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase.