Magneto-optical Kerr effect in Weyl semimetals with broken inversion and time-reversal symmetries

TL;DR

This paper theoretically investigates how axion field modifications in Weyl semimetals with broken symmetries influence the frequency-dependent Kerr rotation and ellipticity angles, considering different experimental configurations and magnetic field conditions.

Contribution

It provides a theoretical analysis of the impact of axion terms on Kerr effects in Weyl semimetals, including in strong magnetic fields and various experimental setups.

Findings

Axion terms modify Kerr rotation and ellipticity angles.

Different behaviors observed in Faraday and Voigt configurations.

Complex frequency dependence in ultra-quantum limit.

Abstract

The topological nature of the band structure of a Weyl semimetal leads to a number of unique transport and optical properties. For example, the description of the propagation of an electromagnetic wave in a Weyl semimetal with broken time-reversal and inversion symmetry, for example, requires a modification of the Maxwell equations by the axion field $\theta \left( \mathbf{r},t\right) =2\mathbf{b}\cdot \mathbf{r}-2b_{0}t,$ where $2% \mathbf{b}$ is the separation in wave vector space between two Weyl nodes of opposite chiralities and $2\hslash b_{0}$ is their separation in energy. In this paper, we study theoretically how the axion terms $b_{0}$ and $\bf{b}$ modify the frequency behavior of the Kerr rotation and ellipticity angles $\theta_{K}\left( \omega \right) $ and $\psi_{K}\left( \omega \right) $ in a Weyl semimetal. Both the Faraday and Voigt configurations are considered since they provide different information on the electronic transitions and plasmon excitation. We derive the Kerr angles firstly without an external magnetic field where the rotation of the polarization is only due to the axion terms and secondly in a strong magnetic field where these terms compete with the gyration effect of the magnetic field. In this latter case, we concentrate on the ultra-quantum limit where the Fermi level lies in the chiral Landau level and the Kerr and ellipticity angles have more complex frequency and magnetic field behaviors.