Infrared probe of the bulk insulating response in Bi 2 − x Sb x Te 3 − y Se y topological insulator alloys

We have investigated the electronic structure and carrier dynamics of the topological insulator $\mathrm{Bi}{}_{2\ensuremath{-}x}\mathrm{Sb}{}_{x}\mathrm{Te}{}_{3\ensuremath{-}y}\mathrm{Se}{}_{y}$, for $x=0.5,y=1.3$ and $x=1,y=2$, using infrared spectroscopy. Our results show that both of these BSTS alloys are highly insulating in the bulk, with analysis of the infrared data indicating an upper limit to the carrier density of $4.4\ifmmode\times\else\texttimes\fi{}{10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Furthermore, analysis of the interband transitions of $\mathrm{Bi}{}_{1.5}\mathrm{Sb}{}_{0.5}\mathrm{Te}{}_{1.7}\mathrm{Se}{}_{1.3}$ revealed distinct band-structure critical points, which suggest high crystallographic order of our crystals. Motivated by the low carrier density and crystallographic order identified in these compounds, we searched for the Landau level transitions associated with the surface states through magneto-optical measurements in the far infrared range. We failed to observe any indications of the Landau level resonances at fields up to 8 T in sharp contrast with our earlier finding for a related $\mathrm{Bi}{}_{1\ensuremath{-}x}\mathrm{Sb}{}_{x}$ alloy. We discuss factors that may be responsible for suppressed magneto-optics response of these single crystals.