Magneto-optical and magnetoelectric effects of topological insulators in quantizing magnetic fields

We develop a theory of the magneto-optical and magnetoelectric 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(T) and nu(B) whereas the low-frequency magnetoelectric 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.