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The optical properties of Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_{2}$S, the mostbulk-insulating topological insulator thus far, have been examined at differenttemperatures over a broad frequency range. No Drude response is detected in thelow-frequency range down to 30~cm$^{-1}$, corroborating the excellentbulk-insulating property of this material. Intriguingly, we observe a sharppeak at about 2\,200~cm$^{-1}$ in the optical conductivity at 5~K. Furtherquantitative analyses of the line shape and temperature dependence of thissharp peak, in combination with first-principles calculations, suggest that itcorresponds to a van Hove singularity arising from Mexican-hat-shaped invertedbands. Such a van Hove singularity is a pivotal ingredient of various stronglycorrelated phases.

Van Hove Singularity Arising from Mexican-Hat-Shaped Inverted Bands in the Topological Insulator Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_{2}$S