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.