Ultrafast transient-photocarrier relaxation through the topological surface state of Bi$_{\mathrm{1.5}}$Sb$_{\mathrm{0.5}}$Te$_{\mathrm{1.7}}$Se$_{\mathrm{1.3}}$

Using optical-pump terahertz-probe spectroscopy, we investigated an ultrafast photocarrier relaxation behavior in a Bi$_{\mathrm{1.5}}$Sb$_{\mathrm{0.5}}$Te$_{\mathrm{1.7}}$Se$_{\mathrm{1.3}}$ (BSTS) single crystal which is one of the most bulk-insulating topological insulators. Compared to n-type bulk-metallic Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$, we found that BSTS endows distinct behaviors in its photocarrier dynamics; (i) the relaxation time turns out to be several times longer, and (ii) the photoconductance exhibits a nonlinear increase as a function of the pumping power. We discuss these intriguing experimental observations based on a bulk-to-surface carrier injection assisted by the built-in electric field near the surface and electron-phonon scattering.