Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field
arXiv:1901.06661 · doi:10.1016/j.aop.2020.168179
Abstract
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.
arXiv commentLatex, 26 pages
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Cited by in corpus (6)
- Chiral Separation effect in non-homogeneous systems
- Effect of interactions on the topological expression for the chiral separation effect
- Equilibrium Chiral Magnetic Effect: spatial inhomogeneity, finite temperature, interactions
- Electric field induced second-order anomalous Hall transport in unconventional Rashba systems
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