  The optical properties of Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_{2}$S, the most
bulk-insulating topological insulator thus far, have been examined at different
temperatures over a broad frequency range. No Drude response is detected in the
low-frequency range down to 30~cm$^{-1}$, corroborating the excellent
bulk-insulating property of this material. Intriguingly, we observe a sharp
peak at about 2\,200~cm$^{-1}$ in the optical conductivity at 5~K. Further
quantitative analyses of the line shape and temperature dependence of this
sharp peak, in combination with first-principles calculations, suggest that it
corresponds to a van Hove singularity arising from Mexican-hat-shaped inverted
bands. Such a van Hove singularity is a pivotal ingredient of various strongly
correlated phases.
