Localization and chiral magnetic effect in quantum diffusive Weyl semimetals

We investigate the effect of disorders on the chiral magnetic effect
(CME) in Weyl semimetals. Based on a minimum two-band model of
the Weyl semimetal, the disorder effect is examined in the quantum
diffusion limit by considering the correction to the CME coefficient due
to the Cooperon channel. It is shown that instead of contributing
through diffusive propagation, the contribution of Cooperon to the CME
coefficient is governed by the sub-diffusive propagation. As a result, unlike
the weak localization and weak antilocalization effects observed in Dirac
fermions, we find that the CME coefficients of finite systems manifest
scalings of strong localization even in three dimension. Our results indicate
that while the chiral magnetic current due to slowly oscillating magnetic fields
can exist in clean systems, it will be strongly suppressed by disorders in
condensed matter systems.