Van Hove singularity arising from Mexican-hat-shaped inverted bands in the topological insulator Sn-doped Bi1.1Sb0.9Te2S

The optical properties of Sn-doped ${\mathrm{Bi}}_1.1{\mathrm{Sb}}_0.9{\mathrm{Te}}₂\mathrm{S}$, 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 $30\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, corroborating the excellent bulk-insulating property of this material. Intriguingly, we observe a sharp peak at about $2200\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ 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.