Maximizing the thermoelectric performance of topological insulator Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ films in the few-quintuple layer regime

Using first-principles calculations and Boltzmann theory, we explore the feasibility to maximize the thermoelectric figure of merit (\textit{ZT}) of topological insulator Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ films in the few-quintuple layer regime. We discover that the delicate competitions between the surface and bulk contributions, coupled with the overall quantum size effects, lead to a novel and generic non-monotonous dependence of \textit{ZT} on the film thickness. In particular, when the system crosses into the topologically non-trivial regime upon increasing the film thickness, the much longer surface relaxation time associated with the robust nature of the topological surface states results in a maximal \textit{ZT} value, which can be further optimized to \textasciitilde 2.0 under physically realistic conditions. We also reveal the appealing potential of bridging the long-standing \textit{ZT} asymmetry of $p$- and $n$-type Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ systems. These findings help to establish intricate connections between the thermoelectric materials and topological insulators.