Topological Superfluids

Abstract

There are many topological faces of the superfluid phases of $^3$He. These superfluids contain various topological defects and textures. The momentum space topology of these superfluids is also nontrivial, as well as the topology in the combined (${\bf p},{\bf r})$ phase space, giving rise to topologically protected Dirac, Weyl and Majorana fermions living in bulk, on the surface and within the topological objects. The nontrivial topology lead to different types of anomalies, which extended in many different directions the Landau-Khalatninkov theory of superfluidity.Comment: 29 pages, 20 figures, 214 references, the draft for the issue of JETP devoted to Khalatnikov-10