Absence of equilibrium chiral magnetic effect

Abstract

We analyse the 3 + 1 D equilibrium chiral magnetic effect (CME). We apply derivative expansion to the Wigner transform of the two -point Green function. This technique allows us to express the response of electric current to external electromagnetic field strength through the momentum space topological invariant. We consider the wide class of the lattice regularizations of quantum field theory (that includes, in particular, the regularization with Wilson fermions) and also certain lattice models of solid state physics (including those of Dirac semimetals). It appears, that in these models the mentioned topological invariant vanishes identically at nonzero chiral chemical potential. That means, that the bulk equilibrium CME is absent in those systems.

Precise Wigner-Weyl calculus for lattice models

“…The meaning of Q(p) for the lattice models of electrons in crystals is the inverse propagator of Bloch electron. Introduction of an external gauge field A(x) defined as a function of coordinates effectively leads to the Peierls substitution (see, for example, [38,78,79]):…”

“…One has in this approximation In a more general case of the homogeneous system withQ = f (p), where f (p) is the function defined in momentum space with periodic boundary conditions, we have Q C (p, x) = f (p). An alternative version of Wigner-Weyl formalism has been proposed in [78,79], although still giving only approximate results for lattice models.…”

Superconductivity Provides Access to the Chiral Magnetic Effect of an Unpaired Weyl Cone

“…The current in the Weyl cone of one chirality has to be canceled by a current in the Weyl cone of opposite chirality to ensure zero net current in equilibrium. The generation of an electrical current density j along an applied magnetic field B, the so-called chiral magnetic effect (CME) [7,8], has been observed as a dynamic, nonequilibrium phenomenon [9][10][11][12][13]-but it cannot be realized in equilibrium because of the fermion doubling [14][15][16][17][18][19][20][21][22][23][24].…”

Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals

“…Consequently, a Weyl semimetal always lacks Lorentz invariance 12 (even if their velocity was equal to the speed of light c), despite exhibiting the z = 1 (E ∼ |k|) scaling of energy-momentum relation. The violation of Lorentz invariance and the existence of nontrivial Berry curvature lead to many anomalous transport and optical properties such as large anomalous Hall effect and optical gyrotropy, and the most peculiar one being the negative longitudinal magnetoresistance due to the chiral or Adler-BellJackiw anomaly [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] .…”