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Non-Abelian Half-Quantum Vortices in ${}^{3}P_{2}$ 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 two-fold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.