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We report on infrared (IR) optical experiments on Bi$_2$Te$_3$ and Mn-dopedBi$_2$Te$_3$ epitaxial thin films. In the latter film, dilute Mn doping (4.5\%)of the topologically nontrivial semiconductor host results intime-reversal-symmetry-breaking ferromagnetic order below $T_C$=15 K. Ourspectroscopic study shows both materials share the Bi$_2$Te$_3$ crystalstructure, as well as classification as bulk degenerate semiconductors. Hencethe Fermi energy is located in the Bi$_2$Te$_3$ conduction band in bothmaterials, and furthermore, there is no need to invoke topological surfacestates to describe the conductivity spectra. We also demonstrate that the Drudeoscillator strength gives a simple metric with which to distinguish thepossibility of topological surface state origins of the low frequencyconductance, and conclude that in both the pristine and Mn-doped Bi$_2$Te$_3$samples the electromagnetic response is indeed dominated by the bulk materialproperties, rather than those of the surface. An encouraging aspect for takingadvantage of the interplay between nontrivial topology and magnetism, however,is that the temperature dependence of the Mn-doped Bi$_2$Te$_3$ film suggestsbulk charge carriers do not play a significant role in mediatingferromagnetism. Thus, a truly insulating bulk may still be suitable for theformation of a ferromagnetic ground state in this dilute magnetic topologicalsemiconductor.

Infrared electrodynamics and ferromagnetism in the topological semiconductors Bi$_2$Te$_3$ and Mn-doped Bi$_2$Te$_3$