Controlling superlong relaxation of photoexcited Dirac fermions in Bi$_2$Te$_2$Se

Among the recently engineered topological insulators (TIs) ternary compound Bi$_2$Te$_2$Se (BTS) displays the highest to-date bulk resistivity (1-6 $\Omega$ cm at 4 K). It is of particular interest in novel photonic and optoelectronic applications owing to the unusually long relaxation time ($\tau > 4~\mu$s) of photoexcited Dirac electrons. Yet, the origin of these long-lived photoexcited carriers, observed by angle- and femtosecond time-resolved photoelectron spectroscopy (tr-ARPES)[1], has not been resolved. Here, we report on transport measurements of electrostatically gated BTS structures which, in conjunction with ARPES studies, demonstrate that $\tau$ is controlled by the subsurface band bending and trap states. As expected from the trap states, gate voltage dependence of BTS resistivity at low temperatures is hysteretic and asymmetric, suggesting that long relaxation times can be ultimately tuned by a charge transfer to the surface. Gating hysteresis can be manipulated by doping BTS with small amounts (1\%) of Sn and by cooling the system under applied gate voltage, pertinent to engineering a lifetime switch for photoexcited Dirac fermions. [1] E. Papalazarou \textit{et al}, preprint (2016).