Half-quantized non-Abelian vortices in neutron 3P2 superfluids inside magnetars

We point out that half-quantized non-Abelian vortices exist as the minimum energy states in rotating neutron $^3P_2$ superfluids in the inner cores of magnetars with magnetic fields greater than $3 \times 10^{15}$ Gauss, while they do not in ordinary neutron stars with smaller magnetic fields. One integer vortex is split into two half-quantized vortices. The number of vortices is about $10^{19}$ and they are separated at about $\mu$m in a vortex lattice for typical parameters, while the vortex core size is about 10–100 fm. They are non-Abelian vortices characterized by a non-Abelian first homotopy group, and consequently when two vortices corresponding to non-commutative elements collide, a rung vortex must be created between them, implying the formation of an entangled vortex network inside the cores of magnetars. We find spontaneous magnetization in the vortex core showing diamagnetism whose typical magnitude is about $10^{8-9}$ Gauss, which is ten times larger than that of integer vortices, when external magnetic fields are present along the vortex line.