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

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 {\mu}VK$^{-1}$, which is an order of magnitude higher than those of the conventional metals and the value is enhanced to -212 {\mu}VK$^{-1}$ 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.