Large thermopower in topological surface state of Sn-BSTS topological insulators: Thermoelectrics and energy-dependent relaxation times

Topological surface Dirac states (TSDSs) generated in three-dimensional topological insulators (3D-TIs) are currently of significant interest for new science and advanced technologies. In contrast to many other thermoelectric materials, 3D-TIs exhibit a significant potential to achieve a large enhancement in thermoelectric power factor ($PF=\ensuremath{\sigma}{S}^{2}$) due to their special topological symmetry. However, only limited experiments and discussions have been made so far for elucidating the thermoelectric properties of TSDS. Herein, we report a large $S$ and $\mathit{PF}$ observed for high-quality single-crystal flakes of $\mathrm{Sn}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{1.1}{\mathrm{Sb}}_{0.9}\mathrm{Te}{\mathrm{S}}_{2}$ (Sn-BSTS). Accurate interpretations that the energy-dependent relaxation times $\ensuremath{\tau}(E)$ play an important role in thermoelectrical transport of 3D-TIs are provided. Among 3D-TIs, Sn-BSTS has the highest bulk insulation and shows intrinsic TSDS transport without bulk contributions, along with its hallmark of quantum integer Hall effect at high temperatures. Based on the longitudinal/transverse electrical transport and the thermoelectric coefficient, $\ensuremath{\tau}(E)\ensuremath{\propto}{E}^{0.21}$ is accurately deduced. As a consequence of the energy-dependent $\ensuremath{\tau}(E)$, a large enhancement in both $S$ and $\mathit{PF}$ is obtained ($S=58\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ and $PF=5.0\phantom{\rule{0.16em}{0ex}}\mathrm{mW}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.28em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ at 77 K), leading to a large increase of 160% for $S$ and 280% for $\mathit{PF}$ when compared to those of graphene at 77 K. The potential thermoelectric performance of the pure TSDS is discussed based on the Boltzmann transport equations.