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 field 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 $μ$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 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 the spontaneous magnetization in the vortex core showing anti-ferromagnetism whose typical magnitude is about $10^{8-9}$ Gauss that is ten times larger than that of integer vortices, when external magnetic fields are present along the vortex line.
Vortex lattice in rotating neutron spin-triplet superfluid
在Ginzburg-Landau极限下，研究了旋转中子自旋三重态超流体中一种可能的无奇异核织构。它是由涡量弥散分布在整个单胞上的非奇异涡格构成的。结果表明，在旋转中子星的核中，非奇异涡旋比一般的线性奇异涡旋更容易出现.所研究的中子系统的序参量属于么正类。这意味着所考虑的超流体不具有自旋极化，并且无核$^{3}$ P $_{2}$涡旋不具有磁化，这使得涡旋的电子散射无效。出于同样的原因，磁通管的钉扎也被抑制。这会影响超流中子星的流体力学。
本文提出了一个中子星壳内中子涡旋的微观量子力学模型。在简要介绍了Bogoliubov- de Gennes方程，这是我们的计算的基础上，我们提出的结果的密度分布，涡核的大小和涡能量，无论是一个孤立的中子涡和涡核重叠的情况下，与一个圆柱形核。证实了涡核尺寸的早期结果，表明涡核尺寸随密度的变化比BCS公式预测的要小得多。
