Optical conductivity of bismuth-based topological insulators

Abstract

The optical conductivity ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ and the spectral weight $SW$ of four topological insulators with increasing chemical compensation (${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3},\phantom{\rule{0.28em}{0ex}}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{2}\mathrm{Te},\phantom{\rule{0.28em}{0ex}}{\mathrm{Bi}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Se}}_{3}$, and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$) have been measured from 5 to 300 K and from subterahertz to visible frequencies. The effect of compensation is clearly observed in the infrared spectra through the suppression of an extrinsic Drude term and the appearance of strong absorption peaks that we assign to electronic transitions among localized states. From the far-infrared spectral weight $SW$ of the most compensated sample (${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$), one can estimate a density of charge carriers on the order of ${10}^{17}/{\mathrm{cm}}^{3}$ in good agreement with transport data. Those results demonstrate that the low-energy electrodynamics in single crystals of topological insulators, even at the highest degree of compensation presently achieved, is still influenced by three-dimensional charge excitations.