Transmission and reflection coefficients and Faraday/Kerr rotations as a function of applied magnetic fields in spin-orbit coupled Dirac metals

Abstract

We reveal the nature of propagation and reflection of light in Weyl metals with broken time reversal symmetry, whose electromagnetic properties are described by axion electrodynamics. These Weyl metals turn out to play the role of a chiral prism: An incident monochromatic wave can split into three waves propagating with different wave numbers, depending on its chirality and polarization (right $\&$ left circular polarizations and linear polarization along the propagating direction). The helicity of the propagating/reflected light is determined by $\textbf{B}_{ext}$ and $\textbf{E}_{light}$, where $\textbf{B}_{ext}$ is the gradient of the $\theta-$field in the axion term given by the applied magnetic field and $\textbf{E}_{light}$ is the electric-field component of the incident light. This implies that the direction of the external magnetic field controls the Faraday/Kerr rotation. In particular, we find that the linear polarization of the oscillating electric field along the propagating direction, which cannot occur in conventional metals, arises when Weyl nodes are aligned along the oscillating magnetic field. We evaluate both transmission/reflection coefficients and Faraday/Kerr rotation angles as a function of both an external magnetic field and frequency for various configurations of light propagation. We propose their strong magnetic-field dependencies as one of the fingerprints of the axion electrodynamics.