Magneto-optical Faraday and Kerr effects in topological insulator films and in other layered quantized Hall systems

We present a theory of the magneto-optical Faraday and Kerr effects of topological insulator (TI) films. For film thicknesses short compared to wavelength, we find that the low-frequency Faraday effect in ideal systems is quantized at integer multiples of the fine structure constant and that the Kerr effect exhibits a giant $\ensuremath{\pi}/2$ rotation for either normal or oblique incidence. For thick films that contain an integer number of half wavelengths, we find that the Faraday and Kerr effects are both quantized at integer multiples of the fine structure constant. For TI films with bulk parallel conduction, we obtain a criterion for the observability of surface-dominated magneto-optical effects. For thin samples supported by a substrate, we find that the universal Faraday and Kerr effects are present when the substrate is thin compared to the optical wavelength or when the frequency matches a thick-substrate cavity resonance. Our theory applies equally well to any system with two conducting layers that exhibit quantum Hall effects.