Chiral magnetic effect in Weyl semimentals and insulators

It has been proposed recently, on the basis of field-theoretical considerations, that the effective electromagnetic action of Weyl semimetals (as well as the closely related Weyl insulators) contains an axion term with the $\theta$-angle dependent on time $t$ or spatial position ${\bf r}$. If correct this would lead to a number of novel observable phenomena, such as the chiral magnetic effect, whereby an applied uniform magnetic field induces a dissipationless bulk current ${\bf j}\propto {\bf B}$. In this work we construct a simple lattice model for a Weyl semimental (insulator) and use it to explicitly test for the chiral magnetic effect by means of numerical techniques combined with analytical calculations. We discuss possible ways to engineer a suitable material in layered nanostructures and comment on the physical observability of the effect.