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Title: Quantum kinetic theory of the chiral anomaly

Abstract

We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field-induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wave-packet dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wave-packet dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. Furthermore we show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.

Authors:
 [1];  [2];  [1]
  1. The Univ. of Texas at Austin, Austin, TX (United States)
  2. The Univ. of New South Wales, Sydney (Australia)
Publication Date:
Research Org.:
Univ. of Texas at Austin, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1511842
Alternate Identifier(s):
OSTI ID: 1414504
Grant/Contract Number:  
FG02-02ER45958; FG03-02ER45958; FG02-ER45958
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 23; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Sekine, Akihiko, Culcer, Dimitrie, and MacDonald, Allan H. Quantum kinetic theory of the chiral anomaly. United States: N. p., 2017. Web. doi:10.1103/physrevb.96.235134.
Sekine, Akihiko, Culcer, Dimitrie, & MacDonald, Allan H. Quantum kinetic theory of the chiral anomaly. United States. doi:10.1103/physrevb.96.235134.
Sekine, Akihiko, Culcer, Dimitrie, and MacDonald, Allan H. Thu . "Quantum kinetic theory of the chiral anomaly". United States. doi:10.1103/physrevb.96.235134. https://www.osti.gov/servlets/purl/1511842.
@article{osti_1511842,
title = {Quantum kinetic theory of the chiral anomaly},
author = {Sekine, Akihiko and Culcer, Dimitrie and MacDonald, Allan H.},
abstractNote = {We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field-induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wave-packet dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wave-packet dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. Furthermore we show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.},
doi = {10.1103/physrevb.96.235134},
journal = {Physical Review B},
number = 23,
volume = 96,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 6 works
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Figures / Tables:

FIG. 1 FIG. 1: (a) Pumping of valley population in a Weyl semimetal by parallel electric and magnetic fields oriented along the $z$ direction in the absence of disorder. When the electronic structure of a Weyl semimetal is approximated by Dirac cones with masses that depend on $k_z$, a magnetic field inducesmore » an anomalous ($N$ = 0) Landau level branch that has only one sign of velocity $v_z$ in a given valley. It follows that in each valley the density of states is increased for states with one sign of velocity and decreased for states with the other sign of velocity, and that the total current summed over a valley is already nonzero in equilibrium. When an electric field drives states through momentum space (diagonal red arrows), the total number of states in a valley varies. (b) Scattering within valleys (curved red arrows) can relax the current in each valley to its equilibrium value, but cannot establish a steady state because the number of states in each valley still changes at a constant rate. A steady state can be established only when intervalley scattering processes are present.« less

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