Abstract

Dirac and Weyl semimetals, whose low-energy quasiparticle excitations are described by the corresponding relativistic-like equations, is an active and vibrant area of research in condensed matter physics. Unusual properties of these materials can be described by various methods ranging from Green’s functions to semiclassical approaches such as the chiral kinetic theory and hydrodynamics.
The possibility of the hydrodynamic regime for electrons in solids is particularly interesting and allows for several unexpected effects related to the flow of electron fluid. Motivated by recent experiments, the consistent hydrodynamics for Weyl quasiparticles is formulated. This framework includes the topological Chern–Simons terms and explicit breaking of the Galilean invariance by the ion lattice. While the Chern–Simons terms do not enter the Navier–Stokes equation directly, they affect electron motion via Maxwell’s equations. It is shown that topological terms quantified by the momentum-space separation between the Weyl nodes lead to a few interesting effects. For example, the hydrodynamic anomalous Hall effect is predicted for a slab of Weyl semimetal. In the case of a nonlocal geometry, electron fluid flow become spatially distorted.
Further, the hydrodynamic description of the Fermi arc surface states is proposed and a few collective modes in the hydrodynamic regime are discussed.