Scattering theory of the chiral magnetic effect in a Weyl semimetal: Interplay of bulk Weyl cones and surface Fermi arcs

Abstract

We formulate a linear response theory of the chiral magnetic effect in a finite Weyl semimetal, expressing the electrical current density $j$ induced by a slowly oscillating magnetic field $B$ or chiral chemical potential $\mu$ in terms of the scattering matrix of Weyl fermions at the Fermi level. Surface conduction can be neglected in the infinite-system limit for $\delta j/\delta \mu$, but not for $\delta j/\delta B$: The chirally circulating surface Fermi arcs give a comparable contribution to the bulk Weyl cones no matter how large the system is, because their smaller number is compensated by an increased flux sensitivity. The Fermi arc contribution to ${\mu }^{-1}\delta j/\delta B$ has the universal value $(e/h{)}^2$, protected by chirality against impurity scattering --- unlike the bulk contribution of opposite sign.

8 pages, 8 figures; V2: added references with discussion; V3: To be published in the Focus Issue on "Topological semimetals" of New Journal of Physics

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• Universal chiral magnetic effect in the vortex lattice of a Weyl superconductor
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• Manifestation of chiral magnetic current in Floquet-Weyl semimetals