  We study a new class of topological charge density wave states exhibiting
monopole harmonic symmetries. The density-wave ordering is equivalent to
pairing in the particle-hole channel due to Fermi surface nesting under
interactions. When electron and hole Fermi surfaces carry different Chern
numbers, the particle-hole pairing exhibits a non-trivial Berry phase inherited
from band structure topology independent of concrete density-wave ordering
mechanism. The associated density-wave gap functions become nodal, and the net
nodal vorticity is determined by the monopole charge of the pairing Berry
phase. The gap function nodes become zero-energy Weyl nodes of the bulk spectra
of quasi-particle excitations. These states can occur in doped Weyl semimetals
with nested electron and hole Fermi surfaces enclosing Weyl nodes of the same
chirality in the weak coupling regime. Topologically non-trivial low-energy
Fermi arc surface states appear in the density-wave ordering state as a
consequence of the emergent zero-energy Weyl nodes.
