Laboratoire de Physique Théorique
Toulouse - UMR 5152

Using derivative expansion applied to the Wigner transform of the two-point Green function, we analyze 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 the ideal tight – binding models of (2+1) D topological insulators. At the same time, using this method, we prove, that in the equilibrium (3+1) D theory the static CME is absent in a certain class of solids, as well as in the properly regularized relativistic quantum field theory.

(Following "Absence of equilibrium chiral magnetic effect," by M.A.Zubkov, Phys. Rev. D 93 (2016) no.10, 105036, doi:10.1103/PhysRevD.93.105036, arXiv:1605.08724 [hep-ph] and "Wigner transformation, momentum space topology, and anomalous transport" by M.A. Zubkov, arXiv:1603.03665 [cond-mat.mes-hall], 10.1016/j.aop.2016.07.011 Annals Phys. 373 (2016) 298-324. )