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

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 $μ$ in terms of the scattering matrix of Weyl fermions at the Fermi level. Surface conduction can be neglected in the infinite-system limit for $δj/δμ$, but not for $δj/δB$: 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 $μ^{-1}δj/δB$ has the universal value $(e/h)^2$, protected by chirality against impurity scattering --- unlike the bulk contribution of opposite sign.