In this contribution we study the magneto-optical Faraday effect of topological insulator (TI) films in the presence of an external magnetic field. In the first part, we give a short review of the essential results [Refs. 10-12] in the low-frequency regime. In strong magnetic fields, the low-frequency Faraday effect for TI thin films is found to be quantized at integer multiples of the fine structure constant. In the second part, we present results from our study on the influence of cyclotron and cavity resonance effects in thick TI films. For thick films, we find that the same quantization of the Faraday rotation re-emerges when cavity resonance occurs. At higher frequencies, the interplay of both cyclotron resonance and cavity resonance effects leads to interesting features in the resulting Faraday rotation.
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