期刊
ANNALS OF PHYSICS
卷 418, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2020.168179
关键词
Wigner-Weyl formalism; Quantum Hall Effect; Topological invariant
Recently the Wigner-Weyl formalism has been applied to the lattice models of solid state physics and to the lattice regularized quantum field theory. This allows to demonstrate that the electric current of intrinsic Anomalous Quantum Hall effect is expressed through the momentum space topological invariant composed of the Green functions both for the two-and the three-dimensional systems. Here we extend this consideration to the case of the Quantum Hall Effect existing in the presence of arbitrarily varying external magnetic field. The corresponding electric current appears to be proportional to the topological invariant in phase space composed of the Wigner transformed Green function that depends both on coordinates and momenta. (C) 2020 Elsevier Inc. All rights reserved.
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