On the absence of equilibrium chiral magnetic effect

Mikhail Zubkov (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We demonstrate how in the fermionic systems the linear response to the external electromagnetic field is related to momentum space topology. We use derivative expansion applied to the Wigner transform of the two - point Green function. It appears, that the response of electric current to the field strength is proportional to momentum space topological invariant. For the $2+1$ D systems this allows to reproduce the well - known expression for Hall conductivity. Next, we analyse for the wide class of the $3+1$ D fermionic systems the equilibrium chiral magnetic effect (CME). For the lattice regularization of continuum quantum field theory (and also for the Dirac semimetals) the mentioned topological invariant does not depend on the value of the chiral chemical potential. That means, that the bulk equilibrium CME is absent in those systems.

Mots clés: chiral magnetic effect; lattice gauge theory; Wigner transform; Momentum space topology; Dirac semimetals

Domaines: Physique [physics]

Mikhail Zubkov. On the absence of equilibrium chiral magnetic effect. 2016. ⟨hal-01275180v2⟩