Chiral Current in the Lattice Model of Weyl Semimetal

We demonstrate the existence of the chiral magnetic effect in a simple lattice model of Weyl semimetal, which is a hallmark of chiral anomaly in the Weyl semimetal, by calculating the anomalous charge current directly. We identify that the uniform external magnetic field can induce a non-dissipative charge current along its direction in Weyl semimetal, even in the absence of an external electric field if the right and left handed Weyl points are separated in energy, and that the anomalous current is proportional to the strength of the magnetic field and the energy separation with a universal coefficient e²/h², which coincide with the ones predicted on the basis of the field theory treatment. Our results give the possibility to detect these nontrivial electrodynamic phenomena in real materials of Weyl semimetal.