High and Magnetic-field-dependent Surface Carriers Mobility in 3D Topological Insulators without Bulk States

Abstract

By applying the conventional two-liquid model to the magnetoresistivity tensor, we reveal a record-high carrier mobility for surface states in tetradymite topological insulators ($\sim$ 20000 cm$^2$/Vs) in both bulk crystals and thin flakes of Sn-Bi$_{1.1}$Sb$_{0.9}$Te$_2$S. Bulk crystals of this 3D topological insulator exhibit a transition from bulk to surface-dominated conductivity below 100 K, whereas in thin flakes, bulk conductivity is suppressed at even higher temperatures. Our data therefore suggest that a key ingredient for elevated mobility is the absence of bulk carriers at the Fermi level. A fingerprint of the high-mobility carriers, i.e a steep low-field magnetoresistance along with a strong Hall effect nonlinearity below 1 T, signifies the presence of at least two surface-related carrier species, even when bulk states are frozen out. To explain the magnetoresistance and the Hall effect in a wider range of magnetic fields ($>1$ T), one must assume that the carrier mobility drops with the field. The influence of Zeeman splitting on mobility and the contribution of anomalous Hall conductivity provide a much better description of the magnetoresistance and the nonlinearity of the Hall coefficient. Our data call for a revision of the surface state mobility in 3D topological insulators.

Figures (8)

• Figure 1: (a) Optical micrograph of the bulk sample mounted for measurements with silver-paint-glued contacts. (b) Scanning electron microscope image of the flake with contacts. (c) Temperature dependencies of the resistivity per square for the flake (red) and bulk crystal samples (blue and green).
• Figure 2: Representative magnetoresistivity $\rho_{xx}(B)$ (a), Hall resistivity $\rho_{xy}(B)$ (b) and Hall coefficient $\rho_{xy}/B(B)$ (c) experimental data for the flake. Panels (d--f) show a comparison of the $\rho_{xx}(B)$, $\rho_{xy}(B)$, and $\rho_{xy}/B(B)$ data at 60 K (black curves), respectively, with two-liquid fits performed in various magnetic field ranges (color curves).
• Figure 3: Temperature dependence of the carrier densities per sheet ($n$; panels a and c) and mobilities ($\mu$; panels b and d) for the Sn-BSTS flake, obtained from the simultaneous fit of $\rho_{xx}(B)$ and $\rho_{xy}(B)$ dependencies with the two-liquid model, as explained in the text. The top panels (a and b) and bottom panels (c and d) show the values for the high- and low-mobility components, respectively.
• Figure 4: Magnetoresistivity (a) and Hall coefficient (b) for the flake at 60 K. Black curves are experimental data, red and green curves are 4- and 5-parameter fits, respectively. Panels (c) and (d) show temperature dependencies of the carrier density and mobility within the 5-parameter fit, respectively.
• Figure S5: Representative magnetoresistivity $\rho_{xx}(B)$ (panels a and c), Hall resistivity $\rho_{xy}(B)$ (panels b and e) and Hall coefficient $\rho_{xy}(B)/B$ (panels c and f) experimental data for the crystals. Panels (a–c) correspond to the 3.2 $\mu$m-thick crystal; panels (d–f) correspond to the 70 $\mu$m-thick crystal.