Theory of Kerr and Faraday rotation in Topological Weyl Semimetals

Topological Weyl semimetals are characterized by bulk Dirac nodes separated in momentum space by a distance $2b$ and lead to Fermi arcs in the surfaces electronic structure. We calculate the Faraday $\theta_F$ and Kerr $\theta_K$ angles for electromagnetic waves scattered from such a Weyl semimetal using the Kubo formalism. (1) For thin films with electromagnetic radiation incident on a surface without arcs, we show that $\theta_K=bd/\alpha\pi$ and $\theta_F=\alpha\pi/bd$ where $\alpha$ is the fine structure constant, and the film thickness $d \ll \lambda$, the wavelength. We further show multiple reflections give rise to giant Kerr rotation, under certain conditions, for a film on a substrate. (2) In the case when the electromagnetic radiation is incident on the surface with arcs, the wave propagating inside the material acquires a longitudinal component of the electric field proportional to $b$. We discuss the implications of our results for thin films of pyrochlore iridates, and also for the recently discovered Dirac semimetals in a magnetic field.