Ultrafast dynamics of Dirac surface and bulk photocarriers in topological-insulator bismuth telluride nanocrystals using terahertz spectroscopy

Unlike conventional semiconductors, Dirac fermions in surface states of topological insulators (TIs) exhibit many fascinating electronic properties relevant for several optoelectronic and spintronic applications. We investigate the relaxation dynamics of photoexcited carriers in bismuth telluride (${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$) nanocrystals---a prominent candidate among the three-dimensional (3D) topological insulators, using ultrafast time resolved terahertz (THz) spectroscopy. Upon photoexcitation using an 800 nm pump pulse, we observe a decrease in the THz transmission due to the absorption of THz radiation by the photoexcited carriers. The time evolution of the real part of pump induced conductivity [$\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})=\phantom{\rule{4pt}{0ex}}{\ensuremath{\sigma}}_{\text{pump}}{\phantom{\rule{4pt}{0ex}}}_{\text{on}}({\ensuremath{\tau}}_{\text{pp}})\ensuremath{-}{\ensuremath{\sigma}}_{\text{pump}}{\phantom{\rule{4pt}{0ex}}}_{\text{off}}$] with respect to the pump-probe delay time (${\ensuremath{\tau}}_{\text{pp}}$), exhibits a sign change from positive to negative as carriers relax back to their equilibrium distribution, which is also evident from the spectral signatures of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}(\ensuremath{\omega})$, measured at various ${\ensuremath{\tau}}_{\text{pp}}$. While the positive sign of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$ is attributed to the contribution from the semiconducting bulk states, the negative sign of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$ at longer delay times is shown to arise from the Dirac surface states of TIs due to increased scattering rate of photoexcited charge carriers. We model the differential conductivity spectrum [$\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}(\ensuremath{\omega})$] and the transient dynamics [$\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$] quantitatively using the Boltzmann transport equation applied to the surface and bulk states. This includes the energy dependence of scattering rates along with the dynamics of hot electron temperature (${T}_{e}$) evaluated in a self-consistent manner. Such an approach enables us to understand various scattering mechanisms associated with the photoexcited carriers both in Dirac surface as well as in bulk electronic states.