### Abstract

For a generic lattice Hamiltonian of the electron states in Weyl semimetals, we calculate the electric charge and current densities in the first order in background electromagnetic and strain-induced pseudoelectromagnetic fields. We show that the resulting expressions for the densities contain contributions of two types. The contributions of the first type coincide with those in the chiral kinetic theory. The contributions of the second type contain the information about the whole Brillouin zone and cannot be reproduced in the chiral kinetic theory. Remarkably, the latter coincide exactly with the Bardeen-Zumino terms that are usually introduced in relativistic quantum field theory in order to define the consistent anomaly. We demonstrate the topological origin of the Bardeen-Zumino (or, equivalently, Chern-Simons) corrections by expressing them in terms of the winding number in the lattice Hamiltonian model.

Original language | English (US) |
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Article number | 085130 |

Journal | Physical Review B |

Volume | 96 |

Issue number | 8 |

DOIs | |

State | Published - Aug 22 2017 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*96*(8), [085130]. https://doi.org/10.1103/PhysRevB.96.085130

**Origin of Bardeen-Zumino current in lattice models of Weyl semimetals.** / Gorbar, E. V.; Miransky, V. A.; Shovkovy, Igor; Sukhachov, P. O.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 96, no. 8, 085130. https://doi.org/10.1103/PhysRevB.96.085130

}

TY - JOUR

T1 - Origin of Bardeen-Zumino current in lattice models of Weyl semimetals

AU - Gorbar, E. V.

AU - Miransky, V. A.

AU - Shovkovy, Igor

AU - Sukhachov, P. O.

PY - 2017/8/22

Y1 - 2017/8/22

N2 - For a generic lattice Hamiltonian of the electron states in Weyl semimetals, we calculate the electric charge and current densities in the first order in background electromagnetic and strain-induced pseudoelectromagnetic fields. We show that the resulting expressions for the densities contain contributions of two types. The contributions of the first type coincide with those in the chiral kinetic theory. The contributions of the second type contain the information about the whole Brillouin zone and cannot be reproduced in the chiral kinetic theory. Remarkably, the latter coincide exactly with the Bardeen-Zumino terms that are usually introduced in relativistic quantum field theory in order to define the consistent anomaly. We demonstrate the topological origin of the Bardeen-Zumino (or, equivalently, Chern-Simons) corrections by expressing them in terms of the winding number in the lattice Hamiltonian model.

AB - For a generic lattice Hamiltonian of the electron states in Weyl semimetals, we calculate the electric charge and current densities in the first order in background electromagnetic and strain-induced pseudoelectromagnetic fields. We show that the resulting expressions for the densities contain contributions of two types. The contributions of the first type coincide with those in the chiral kinetic theory. The contributions of the second type contain the information about the whole Brillouin zone and cannot be reproduced in the chiral kinetic theory. Remarkably, the latter coincide exactly with the Bardeen-Zumino terms that are usually introduced in relativistic quantum field theory in order to define the consistent anomaly. We demonstrate the topological origin of the Bardeen-Zumino (or, equivalently, Chern-Simons) corrections by expressing them in terms of the winding number in the lattice Hamiltonian model.

UR - http://www.scopus.com/inward/record.url?scp=85029710510&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevB.96.085130

DO - 10.1103/PhysRevB.96.085130

M3 - Article

VL - 96

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 8

M1 - 085130

ER -