Magneto-optical and Magneto-electric Effects of Topological Insulators in Quantizing Magnetic Fields

TL;DR

This paper develops a theoretical framework for understanding the magneto-optical and magneto-electric effects in topological insulator thin films under strong magnetic fields, revealing quantized Faraday rotation and dependence on surface state filling factors.

Contribution

The study introduces a comprehensive theory linking surface state filling factors to magneto-optical and magneto-electric responses in topological insulators under quantizing magnetic fields.

Findings

Faraday rotation is quantized in integer multiples of the fine structure constant.

Kerr effect exhibits a π/2 rotation at low frequencies.

High-frequency cyclotron-resonance features depend on surface filling factors.

Abstract

We develop a theory of the magneto-optical and magneto-electric properties of a topological insulator thin film in the presence of a quantizing external magnetic field. We find that low-frequency magneto-optical properties depend only on the sum of top and bottom surface Dirac-cone filling factors $\nu_{\mathrm{T}}$ and $\nu_{\mathrm{B}}$, whereas the low-frequency magneto-electric response depends only on the difference. The Faraday rotation is quantized in integer multiples of the fine structure constant and the Kerr effect exhibits a $\pi/2$ rotation. Strongly enhanced cyclotron-resonance features appear at higher frequencies that are sensitive to the filling factors of both surfaces. When the product of the bulk conductivity and the film thickness in $e^2/h$ units is small compared to $\alpha$, magneto-optical properties are only weakly dependent on accidental doping in the interior of the film.