Topological invariant for superfluid 3He-B and quantum phase transitions

TL;DR

This paper introduces a topological invariant for superfluid 3He-B, linking its vacuum states to topological classifications and Majorana fermions, with implications for understanding quantum phase transitions.

Contribution

It defines an integer-valued topological invariant for superfluid 3He-B using Green's functions, accounting for interactions and discrete symmetries.

Findings

Classifies vacuum states of superfluid 3He-B topologically.

Identifies additional subclasses due to discrete symmetries.

Connects topological invariants to Majorana fermions at interfaces.

Abstract

We consider topological invariant describing the vacuum states of superfluid 3He-B, which belongs to the special class of time-reversal invariant topological insulators and superfluids. Discrete symmetries important for classification of the topologically distinct vacuum states are discussed. One of them leads to the additional subclasses of 3He-B states and is responsible for the finite density of states of Majorana fermions living at some interfaces between the bulk states. Integer valued topological invariant is expressed in terms of the Green's function, which allows us to consider systems with interaction.