### 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.

Original language | English (US) |
---|---|

Article number | 205119 |

Journal | Physical Review B |

Volume | 97 |

Issue number | 20 |

DOIs | |

State | Published - May 14 2018 |

### Fingerprint

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*97*(20), [205119]. https://doi.org/10.1103/PhysRevB.97.205119

**Hydrodynamic electron flow in a Weyl semimetal slab : Role of Chern-Simons terms.** / Gorbar, E. V.; Miransky, V. A.; Shovkovy, Igor; Sukhachov, P. O.

Research output: Contribution to journal › Review article

*Physical Review B*, vol. 97, no. 20, 205119. https://doi.org/10.1103/PhysRevB.97.205119

}

TY - JOUR

T1 - Hydrodynamic electron flow in a Weyl semimetal slab

T2 - Role of Chern-Simons terms

AU - Gorbar, E. V.

AU - Miransky, V. A.

AU - Shovkovy, Igor

AU - Sukhachov, P. O.

PY - 2018/5/14

Y1 - 2018/5/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85046994003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046994003&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.97.205119

DO - 10.1103/PhysRevB.97.205119

M3 - Review article

VL - 97

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 20

M1 - 205119

ER -