Abstract: 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.

Key words: ?-mapping topological current theory, topological classification, Weyl semimetals, non-Hermitian systems