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

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.

23 pages, 6 multi-panel figures; published version

References in corpus (23)

• The Chiral Magnetic Effect
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Charge separation induced by P-odd bubbles in QCD matter
• Theory of universal incoherent metallic transport
• Anomalous Hall Effect in Weyl Metals
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Hydrodynamics of electrons in graphene
• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Relativistic Hydrodynamics with General Anomalous Charges
• Lorentz Invariance in Chiral Kinetic Theory
• Slow imbalance relaxation and thermoelectric transport in graphene
• The chiral magnetic effect in hydrodynamical approach
• Rare region effects dominate weakly disordered 3D Dirac points
• Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
• Quantum Transport in Topological Semimetals under Magnetic Fields
• Electron hydrodynamics dilemma: whirlpools or no whirlpools
• Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons
• Microscopic theory for electron hydrodynamics in monolayer and bilayer graphene
• Chiral asymmetry of the Fermi surface in dense relativistic matter in a magnetic field
• Consistent hydrodynamic theory of chiral electrons in Weyl semimetals
• Stable Weyl points, trivial surface states and particle-hole compensation in WP2
• Origin of Bardeen-Zumino current in lattice models of Weyl semimetals

Cited by in corpus (15)

• Hydrodynamic approach to two-dimensional electron systems
• Skin effect as a probe of transport regimes in Weyl semimetals
• Nonlocal transport in Weyl semimetals in the hydrodynamic regime
• Optical signatures of shear collective modes in strongly interacting Fermi liquids
• Hydrodynamics of Fermi arcs: Bulk flow and surface collective modes
• Chiral magnetic response to arbitrary axial imbalance
• Magnetotransport and internodal tunnelling in Weyl semimetals
• Quantum Kinetic Theory with Vector and Axial Gauge Fields
• Anomalous Gurzhi effect
• Phonon-mediated Hydrodynamic Transport in a Weyl Semimetal
• Weyl hydrodynamics in a strong magnetic field
• Rotating solutions of nonideal transverse Chern-Simons magnetohydrodynamics and the anomalous Hall current
• Stray magnetic field and stability of time-dependent viscous electron flow
• Viscoelastic response and anisotropic hydrodynamics in Weyl semimetals
• Chiral Anomaly Trapped in Weyl Metals: Nonequilibrium Valley Polarization at Zero Magnetic Field