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

Topological insulators show novel magneto-electric effect when the surface Dirac cone dispersion is gapped by a weak Zeeman field. In this talk, we present our study of the magneto-optical and magneto-electric effects of a thin-film topological insulator in the presence of a strong quantizing magnetic field. We find that low-frequency magneto-optical properties depend only on the sum of top and bottom surface Dirac-cone filling factors, whereas the magneto-electric response depends only on the difference. The Faraday rotation is quantized in integer multiples of the fine structure constant $\alpha$ and the Kerr effect exhibits a full-quarter 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.