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 spin-orbit coupled Dirac metals under external magnetic fields. Such applied magnetic fields split the fourfold degeneracy of a spin-orbit coupled Dirac metal state into a pair of a twofold degeneracy along the direction of the applied magnetic field, resulting in a Weyl band structure. These Weyl metals turn out to play the role of a chiral prism, whose electromagnetic properties are described by axion electrodynamics: An incident monochromatic wave can split into three differently polarized modes (eigenvectors), propagating with different wave numbers (eigenvalues). In particular, the axion electrodynamics allows the longitudinal component naturally inside the Weyl metal state. 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. The helicity of the propagating/reflected light is determined by del theta x E-light = B-ext x E-light, where del theta = B-ext is the gradient of the theta field in the axion term given by the applied magnetic field and & gin is the electric field of the incident light. This implies that the direction of the external magnetic field controls the Faraday/Kerr rotation. We find several interesting optical properties of the Weyl metal phase. First, longitudinal oscillating charge density fluctuations along the light propagating direction arise when the pair of Weyl nodes are aligned along the direction of the oscillating magnetic field, which gives rise to the longitudinal component of the electromagnetic wave. Second, the Weyl metal phase becomes more reflective when the external magnetic field is enhanced to be along with E//B-ext due to the longitudinal negative magnetoresistivity, which is a fingerprint of the Weyl metal phase. Third, eigen-modes can have various structures, depending on a parameter eta which corresponds to a ratio between the conventional Hall effect from normal electrons and the anomalous Hall effect from Weyl electron. We propose these strong magnetic field dependencies of the optical response as the fingerprints of the axion electrodynamics.