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Wigner transformation, momentum space topology, and anomalous transport

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.
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https://hal.archives-ouvertes.fr/hal-01387618
Contributor : Mikhail Zubkov <>
Submitted on : Tuesday, October 25, 2016 - 6:31:18 PM
Last modification on : Thursday, March 5, 2020 - 5:33:18 PM

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M Zubkov. Wigner transformation, momentum space topology, and anomalous transport. Annals of Physics, 2016, 373, pp.298 - 324. ⟨10.1016/j.aop.2016.07.011⟩. ⟨hal-01387618⟩

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