用 ϕ-映射拓扑流理论对厄米及非厄米 Weyl 半金属进行拓扑分类. 对一个给定的哈 密顿, 在动量空间建立一个由自旋组成的ϕ场, 再由这个 ⇀ ϕ 场给出拓扑荷密度分布. 发现只 有在 ϕ场模的零点, 拓扑荷密度的值才不为零, 而这些 ϕ场模的零点其实就是 Weyl 点或 Weyl 奇异点所在位置. 通过对拓扑荷密度的积分, 得到了可用于对系统进行拓扑分类的整数拓扑数.

In this study, we examine the topological classification of Weyl semimetals of Hermitian and non-Hermitian systems using ϕ-mapping topological current theory. We establish the ϕ fields in the momentum space by the given Hamiltonians of two-band systems to define the topological charge density. We find that the topological charge density is nonzero only at the zeroes of the norm of the ϕ fields, and these zeroes are exactly where Weyl points or Weyl exceptional points are located. The quantized numbers obtained by integrating the topological charge density can be used as the topological numbers for topo- logical classification.