### 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.

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

Article number | 121105 |

Journal | Physical Review B |

Volume | 97 |

Issue number | 12 |

DOIs | |

State | Published - Mar 12 2018 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*97*(12), [121105]. https://doi.org/10.1103/PhysRevB.97.121105

**Consistent hydrodynamic theory of chiral electrons in weyl semimetals.** / Gorbar, E. V.; Miransky, V. A.; Shovkovy, Igor; Sukhachov, P. O.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 97, no. 12, 121105. https://doi.org/10.1103/PhysRevB.97.121105

}

TY - JOUR

T1 - Consistent hydrodynamic theory of chiral electrons in weyl semimetals

AU - Gorbar, E. V.

AU - Miransky, V. A.

AU - Shovkovy, Igor

AU - Sukhachov, P. O.

PY - 2018/3/12

Y1 - 2018/3/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85043992848&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043992848&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.97.121105

DO - 10.1103/PhysRevB.97.121105

M3 - Article

VL - 97

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 12

M1 - 121105

ER -