  The topological magneto-electric effect (TME) is a characteristic property of
topological insulators. In this article, we use a simplified coupled-Dirac-cone
electronic structure model to theoretically evaluate the THz and far infrared
Kerr and Faraday responses of thin films of MnBi$_2$Te$_4$ with up to $N=10$
septuple layers with the goal of clarifying the relationship between these
convenient magneto-optical observables and the TME. We find that for even $N$
the linear Kerr and Faraday responses to an electric field vanish in the
low-frequency limit, even though the magnetoelectric response is large and
approximately quantized.
