Electromagnetic fields induced by an electric charge near a Weyl semimetal

Weyl semimetals (WSM) are a new class of topological materials that exhibit a bulk Hall effect and a chiral magnetic effect. The topological contribution of these unusual electromagnetic responses can be characterized by an axion term θE·B with space and time dependent axion angle θ(r,t). In this paper we compute the electromagnetic fields produced by an electric charge near a topological Weyl semimetal with two Weyl nodes, in the equilibrium state, at zero electric chemical potential, and with broken time-reversal symmetry. We find that, as in ordinary metals and dielectrics, outside the WSM the electric field is mainly determined by the optical properties of the material. The magnetic field is, on the contrary, of topological origin due to the magnetoelectric effect of topological phases. We show that the magnetic field exhibits an interesting behavior above the WSM as compared with that induced above a topological insulator: the field lines begin at the surface and then end at the surface (but not at the same point). This distinctive behavior of the magnetic field is an experimentally observable signature of the anomalous Hall effect in the bulk of the WSM. We discuss two experimental setups for testing our predictions of the induced magnetic field.