Ultrathin films of three-dimensional topological insulators by vapor-phase epitaxy: Surface dominant transport in a wide temperature range as revealed by measurements of the Seebeck effect

Realization of intrinsic surface dominant transport in a wide temperature region for topological insulators (TIs) is an important frontier research to promote the progress of TIs toward future electronics. We report here systematic measurements of longitudinal electrical transport, Shubnikov--de Haas (SdH) quantum oscillations, the Hall coefficient (${R}_{\mathrm{H}}^{2\mathrm{D}}$), and the Seebeck coefficient as a function of film thickness ($d$) and temperature using high-quality $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}x}\mathrm{S}{\mathrm{b}}_{x}\mathrm{T}{\mathrm{e}}_{3\ensuremath{-}y}\mathrm{S}{\mathrm{e}}_{y}$ single-crystal thin films grown by physical vapor-phase deposition. The thickness dependence of sheet conductance and the Seebeck coefficient clearly shows the suppression of semiconducting hole carriers of bulk states by reducing film thickness, reaching to the surface dominant transport at below ${d}_{\mathrm{c}}=14\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. Quantitative arguments are made as to how the contribution of itinerant carrier number ($n$) can be suppressed, using both ${R}_{\mathrm{H}}^{2\mathrm{D}}$ (${n}_{\mathrm{Hall}}^{2\mathrm{D}}$) and SdH (${n}_{\mathrm{SdH}}$). Intriguingly, the value of ${n}_{\mathrm{Hall}}^{2\mathrm{D}}$ approaches being twice that of ${n}_{\mathrm{SdH}}$ below ${d}_{\mathrm{c}}$. While ${R}_{\mathrm{H}}^{2\mathrm{D}}$ shows a negative sign in the whole temperature region, a change from negative to positive polarity is clearly observed for $S$ at high temperatures when $d$ is thick. We point out that this inconsistency observed between ${R}_{\mathrm{H}}^{2\mathrm{D}}$ and $S$ is intrinsic in three-dimensional (3D) TIs and its origin is the large difference in carrier mobility between the bulk and the topological surface. We propose that the Seebeck coefficient can become a convenient and effective tool to evaluate the intrinsic topological surface transport of 3D TIs in the absence of magnetic field.