Chiral Magnetic Effect in finite-size samples of parity-breaking Weyl semimetals

We study the static electric current due to the Chiral Magnetic Effect in samples of Weyl semimetals with slab geometry, where the magnetic field is parallel to the boundaries of the slab. We use the Wilson-Dirac Hamiltonian as a simplest model of parity-breaking Weyl semimetal with two-band structure. We find that the CME current is strongly localized at the open boundaries of the slab, where the current density in the direction of the magnetic field approaches the conventional value $j = \mu_5 B /2 \pi^2$ at sufficiently small values of the chiral chemical potential $\mu_5$ and magnetic field $B$. On the other hand, very large values of magnetic field tend to suppress the CME response. We observe that the localization width of the current is independent of the slab width and is given by the magnetic length $l_B = 1/\sqrt{B}$ when $\mu_5 \ll \sqrt{B}$. In the opposite regime when $\mu_5 \gg \sqrt{B}$ the localization width is determined solely by $\mu_5$