Temperature-dependent terahertz conductivity of topological insulator Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2}$

Using Terahertz Time-Domain Spectroscopy, we study the temperature-dependent complex optical conductivity of the topological insulator, Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2}$ single-crystal from 5 K to 150 K in the terahertz regime (0.4 -- 3.0 THz). We analyze our experimental results using the Drude-Lorentz model, with the Drude component representing the metallic surface state and the Lorentz term representing the bulk insulating state. We find the conductivity to be dominated by the Drude contribution, suggesting the presence of metallic surface states. The low-frequency real conductivity follows a thermally-activated behavior. Its origin is also discussed.