Title: Consistent hydrodynamic theory of chiral electrons in Weyl semimetals,
Abstract: The complete set of Maxwell's and hydrodynamic equations for the chiral
electrons in Weyl semimetals is presented. The formulation of the Euler
equation takes into account the explicit breaking of the Galilean invariance by
the ion lattice. It is shown that the Chern-Simons (or Bardeen-Zumino)
contributions should be added to the electric current and charge densities in
Maxwell's equations that provide the information on the separation of Weyl
nodes in energy and momentum. On the other hand, these topological
contributions do not directly affect the Euler equation and the energy
conservation relation for the electron fluid. By making use of the proposed
consistent hydrodynamic framework, we show that the Chern-Simons contributions
strongly modify the dispersion relations of collective modes in Weyl
semimetals. This is reflected, in particular, in the existence of distinctive
anomalous Hall waves, which are sustained by the local anomalous Hall currents.