Non-Abelian Half-Quantum Vortices in ${}^{3}P_{2}$ Topological Superfluids

TL;DR

This paper demonstrates the existence and stability of non-Abelian half-quantum vortices with Majorana fermions in ${}^{3}P_{2}$ superfluids relevant to neutron stars, revealing novel topological quantum phenomena.

Contribution

It establishes the stability of non-Abelian HQVs in ${}^{3}P_{2}$ superfluids and identifies Majorana fermions on these vortices, a new topological feature.

Findings

Singly quantized vortices split into pairs of non-Abelian HQVs

Majorana fermions are localized on each HQV

Topologically protected non-Abelian anyons are present

Abstract

${}^{3}P_{2}$ superfluids realized in neutron stars are the largest topological quantum matters in our Universe. We establish the existence and stability of non-Abelian half-quantum vortices (HQVs) in ${}^{3}P_{2}$ superfluids with strong magnetic fields. Using a self-consistent microscopic approach, we find that a singly quantized vortex is energetically destabilized into a pair of two non-Abelian HQVs owing to the strongly spin-orbit-coupled pairing. We find a topologically protected Majorana fermion on each HQV, thereby providing two-fold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.