Optical conductivity of bismuth-based topological insulators

The optical conductivity σ₁(ω) and the spectral weight $SW$ of four topological insulators with increasing chemical compensation (${Bi}₂{Se}₃,{{0.28em}{0ex}}{Bi}₂{Se}₂Te,{{0.28em}{0ex}}{Bi}_{2{-}x}{Ca}ₓ{Se}₃$, and ${Bi}₂{Te}₂Se$) 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 (Bi₂Te₂Se), one can estimate a density of charge carriers on the order of 10¹⁷/cm³ 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.