Wigner transformation, momentum space topology, and anomalous transport

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42 Scopus citations


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
StatePublished - 1 Oct 2016
Externally publishedYes


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


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