Landau level spectroscopy of Bi$_2$Te$_3$

Here we report on Landau level spectroscopy in magnetic fields up to 34 T performed on a thin film of topological insulator Bi$_2$Te$_3$ epitaxially grown on a BaF$_2$ substrate. The observed response is consistent with the picture of a direct-gap semiconductor in which charge carriers closely resemble massive Dirac particles. The fundamental band gap reaches $E_g=(175\pm 5)$~meV at low temperatures and it is not located on the trigonal axis, thus displaying either six or twelvefold valley degeneracy. Notably, our magneto-optical data do not indicate any band inversion. This suggests that the fundamental band gap is relatively distant from the $\Gamma$ point where profound inversion exists andgives rise to relativistic-like surface states of Bi$_2$Te$_3$.