Non-Abelian half-quantum vortices in 3P2 topological superfluids

${}³{P}₂$ 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 twofold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.