Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state.

Ken N Okada,Kei S Takahashi,Atsushi Tsukazaki,Yoshinori Tokura,Masataka Mogi,Masashi Kawasaki,Youtarou Takahashi,Naoki Ogawa,Ryutaro Yoshimi

doi:10.1038/ncomms12245

Abstract

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit.

Highlights

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism
Quantized magnetoelectric responses are predicted on the quantum anomalous Hall (QAH) state induced by the magnetic mass-gap on the surface Dirac cone under the broken time-reversal symmetry
The observation of genuine topological magnetoelectric (TME) signal is limited to the low energy, that is, sufficiently lower than the magnetic mass-gap to avoid the responses from real electronic transitions

Summary

Introduction

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. Phenomena, QAH effect and topological Faraday and Kerr rotations, are observed as quantization of different physical quantities; sxy 1⁄4 e2/h and yF 1⁄4 a 1⁄4 2pe2/hc.

Results

Conclusion