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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.
Forward citations
Cited by 2 Pith papers
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Effective Lagrangian for the macroscopic motion of Weyl fermions in $^3$He-A
Derives a macroscopic-motion effective Lagrangian for Weyl fermions in 3He-A and uses it to compute equilibrium thermodynamics around integer mass vortices.
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Topological invariant responsible for the integer QHE and non-commutative geometry
The integer quantum Hall invariant N3 is expressed as a K-theory/cyclic-cohomology pairing; it vanishes on finite lattices and is only conditionally integer in the infinite-lattice limit.
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