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.

6+8 pages, 1 figure; published version; a few minor typos in the definitions of $d_z$ and $b_0$ are corrected

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Cited by in corpus (28)

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• Chirality-dependent planar Hall effect in inhomogeneous Weyl semimetals
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Anomalous Hydrodynamic Transport in Interacting Noncentrosymmetric Metals
• Dynamo Effect and Turbulence in Hydrodynamic Weyl Metals
• Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms
• Charge-spin response and collective excitations in Weyl semimetals
• Collective excitations in Weyl semimetals in the hydrodynamic regime
• Helical magnetic effect and the chiral anomaly
• Nonlocal transport in Weyl semimetals in the hydrodynamic regime
• Hydrodynamics of Fermi arcs: Bulk flow and surface collective modes
• Chiral magnetic response to arbitrary axial imbalance
• Magnetotransport and internodal tunnelling in Weyl semimetals
• Nonreciprocal electron hydrodynamics under magnetic fields: applications to nonreciprocal surface magnetoplasmons
• Quantum Kinetic Theory with Vector and Axial Gauge Fields
• Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
• Plasmonic quantum nonlinear Hall effect in noncentrosymmetric 2D materials
• Holographic Charged Fluid with Chiral Electric Separation Effect
• Anomalous Gurzhi effect
• Duality between disordered nodal semimetals and systems with power-law hopping
• Weyl hydrodynamics in a strong magnetic field
• Phonon-mediated Hydrodynamic Transport in a Weyl Semimetal
• Rotating solutions of nonideal transverse Chern-Simons magnetohydrodynamics and the anomalous Hall current
• Heat transport in Weyl semimetals in the hydrodynamic regime
• Viscoelastic response and anisotropic hydrodynamics in Weyl semimetals
• Stokes flow in an electronic fluid with odd viscosity
• Entropy Wave Instability in Dirac and Weyl Semimetals
• Nonlocal transport phenomena in Weyl metals beyond the mesoscopic scale