Wigner transformation, momentum space topology, and anomalous transport

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Abstract

Using derivative expansion applied to the Wigner transform of the two- point Green function we analyse the anomalous quantum Hall effect (AQHE), and the chiral magnetic effect (CME). The corresponding currents are proportional to the momentum space topological invariants. We reproduce the conventional expression for the Hall conductivity in 2+1 D. In 3+1 D our analysis allows to explain systematically the AQHE in topological insulators and Weyl semimetals. At the same time using this method it may be proved, that the equilibrium CME is absent in the wide class of solids, as well as in the properly regularized relativistic quantum field theory.

Original languageEnglish
Pages (from-to)298-324
Number of pages27
JournalAnnals of Physics
Volume373
DOIs
StatePublished - 1 Oct 2016
Externally publishedYes

Keywords

  • Anomalous quantum Hall effect
  • Chiral magnetic effect
  • Momentum space topology
  • Topological insulators
  • Weyl semimetals
  • Wigner transformation

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