Landau level spectroscopy of surface states in the topological insulator Bi${}_{0.91}$Sb${}_{0.09}$ via magneto-optics

We have performed broad-band zero-field and magneto-infrared spectroscopy of the three dimensional topological insulator Bi${}_{0.91}$Sb${}_{0.09}$. The zero-field results allow us to measure the value of the direct band gap between the conducting $L_a$ and valence $L_s$ bands. Under applied field in the Faraday geometry (\emph{k} $\mathrm{\mid }\mathrm{\mid }$ \emph{H} $\mathrm{\mid }\mathrm{\mid }$ C1), we measured the presence of a multitude of Landau level (LL) transitions, all with frequency dependence $\omega \propto \sqrt{H}$. We discuss the ramification of this observation for the surface and bulk properties of topological insulators.