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 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 -1δj/δB has the universal value (e/h)2, protected by chirality against impurity scattering - unlike the bulk contribution of opposite sign.