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 $\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.

Keywords

• Weyl semimetal
• chiral magnetic effect
• scattering theory
• Fermi arcs
• surface contribution