  Magnetic orders characterized by multiple ordering vectors harbor
noncollinear and noncoplanar spin textures and can be a source of unusual
electronic properties through the spin Berry phase mechanism. We theoretically
show that such multiple-$Q$ states are stabilized in itinerant magnets in the
form of superpositions of collinear up-up-down-down (UUDD) spin states, which
accompany the density waves of vector and scalar chirality. The result is drawn
by examining the ground state of the Kondo lattice model with classical
localized moments, especially when the Fermi surface is tuned to be partially
nested by the symmetry-related commensurate vectors. We unveil the instability
toward the multiple-$Q$ UUDD states with chirality density waves, using the
perturbative theory, variational calculations, and large-scale Langevin
dynamics simulations. We also show that the chirality density waves can induce
rich nontrivial topology of electronic structures, such as the massless Dirac
semimetal, Chern insulator with quantized topological Hall response, and
peculiar edge states which depend on the phase of chirality density waves at
the edges.
