Thermoelectric properties of 3D topological insulator: Direct observation of topological surface and its gap opened states

Abstract

We report thermoelectric (TE) properties of topological surface Dirac states (TSDS) in three-dimensional topological insulators (3D-TIs) purely isolated from the bulk by employing single crystal Bi${}_{2-x}$Sb${}_x$Te${}_{3-y}$Se${}_y$ films epitaxially grown in the ultrathin limit. Two intrinsic nontrivial topological surface states, a metallic TSDS (m-TSDS) and a gap-opened semiconducting topological state (g-TSDS), are successfully observed by electrical transport, and important TE parameters (electrical conductivity ($\sigma$), thermal conductivity ($\kappa$), and thermopower ($S$)) are accurately determined. Pure m-TSDS gives $S$=-44 μVK${}^{-1}$, which is an order of magnitude higher than those of the conventional metals and the value is enhanced to -212 μVK${}^{-1}$ for g-TSDS. It is clearly shown that the semi-classical Boltzmann transport equation (SBTE) in the framework of constant relaxation time ($\tau$) most frequently used for conventional analysis cannot be valid in 3D-TIs and strong energy dependent relaxation time $\tau (E)$ beyond the Born approximation is essential for making intrinsic interpretations. Although $\sigma$ is protected on the m-TSDS, $\kappa$ is greatly influenced by the disorder on the topological surface, giving a dissimilar effect between topologically protected electronic conduction and phonon transport.

15 pages, 4 figures