Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms

TL;DR

This paper investigates the hydrodynamic behavior of electron flow in Weyl semimetals, highlighting how topological Chern-Simons terms influence flow profiles, Hall currents, and surface potentials under external electric fields.

Contribution

It introduces a comprehensive hydrodynamic model for Weyl semimetals that incorporates topological effects and dynamical electromagnetism, revealing novel flow and current phenomena.

Findings

Nonuniform electron flow profile with a dissipating component across the slab.

Topological Chern-Simons terms modify the anomalous Hall current.

Hydrodynamic flow induces a surface electric potential difference.

Abstract

The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab of finite thickness is studied by using the consistent hydrodynamic theory. The latter includes viscous, anomalous, and vortical effects, as well as accounts for dynamical electromagnetism. The energy and momentum separations between the Weyl nodes are taken into account via the topological Chern-Simons contributions in the electric current and charge densities in Maxwell's equations. When an external electric field is applied parallel to the slab, it is found that the electron fluid velocity has a nonuniform profile determined by the viscosity and the no-slip boundary conditions. Most remarkably, the fluid velocity field develops a nonzero component across the slab that gradually dissipates when approaching the surfaces. This abnormal component of the flow arises due to the anomalous Hall voltage induced by the topological Chern-Simons current. Another signature feature of the hydrodynamics in Weyl semimetals is a strong modification of the anomalous Hall current along the slab in the direction perpendicular to the applied electric field. Additionally, it is found that the topological current induces an electric potential difference between the surfaces of the slab that is strongly affected by the hydrodynamic flow.