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The spectrum of collective excitations in Weyl materials is studied by using a consistent hydro- dynamics. The corresponding framework includes the vortical and chiral anomaly effects, as well as the dependence on the separation between the Weyl nodes in energy b0 and momentum b. The latter are introduced via the Chern–Simons contributions to the electric current and charge densities in the Maxwell’s equations. It is found that, even in the absence of a background magnetic field, certain collective excitations (e.g., the helicon-like modes and anomalous Hall waves) are strongly affected by the chiral shift b. In a background magnetic field, the existence of distinctive longi- tudinal and transverse anomalous Hall waves with a linear dispersion relation is predicted. They originate from the oscillations of the electric charge density and electromagnetic fields, in which different components of the fields are connected via the anomalous Hall effect in Weyl semimetals.more » « less
