Consistent hydrodynamic theory of chiral electrons in Weyl semimetals

TL;DR

This paper develops a comprehensive hydrodynamic and electromagnetic framework for chiral electrons in Weyl semimetals, incorporating topological effects and revealing novel collective modes like anomalous Hall waves.

Contribution

It introduces a consistent hydrodynamic theory that includes topological Chern-Simons contributions, clarifying their role in Weyl semimetals' electrodynamics.

Findings

Chern-Simons contributions modify collective mode dispersion relations

Existence of anomalous Hall waves sustained by local currents

Hydrodynamic equations account for explicit lattice effects

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.