Absence of strong localization at low conductivity in the topological surface state of low-disorder ${\mathrm{Sb}}_2{\mathrm{Te}}_3$

We present low-temperature transport measurements of a gate-tunable thin-film topological insulator system that features high mobility and low carrier density. Upon gate tuning to a regime around the charge neutrality point, we infer an absence of strong localization even at conductivities well below $e^2/h$, where two-dimensional electron systems should conventionally scale to an insulating state. Oddly, in this regime the localization coherence peak lacks conventional temperature broadening, though its tails do change dramatically with temperature. Using a model with electron-impurity scattering, we extract values for the disorder potential and the hybridization of the top and bottom surface states.

Figure 1

Transport properties. (a) Longitudinal conductivity as a function of top gate voltage at zero field and $T=1.6\text{K}$. The top axis shows the actual gate voltage; the bottom axis shows the difference $\mathrm{\Delta }V$ between the gate voltage and the conductivity minimum $V_{\text{min}}$. Inset: The conductivity at $V_{\text{min}}$ is described by an Arrhenius law plus a constant offset, which we attribute to Joule heating from the current bias. (b) Carrier density (left axis) extracted from the Hall slope, and the associated Hall mobility (right axis), shown vs $\mathrm{\Delta }V$ at $T=1.6\text{K}$. Fits to the slope of the density (solid lines) yield ${\alpha }_h=2.3\times {10}^{11}{\text{cm}}^{-2}/\text{V}$ on the hole side and ${\alpha }_e=1.7\times {10}^{10}{\text{cm}}^{-2}/\text{V}$ on the electron side.

Figure 2

Magnetoconductance, indicating weak antilocalization. (a)–(d) Differential longitudinal conductivity $\mathrm{\Delta }{\sigma }_{xx}(T,H)\equiv {\sigma }_{xx}(T,H)-{\sigma }_{xx}(T,0)$ vs magnetic field at temperatures between 1.6 and $30\text{K}$ at (a) $V_g-V_{\text{min}}=-8\text{V}$, (b) $-4\text{V}$, (c) $0\text{V}$, and (d) $4\text{V}$.

Figure 3

Crossover of the quantum transport correction from weak antilocalization to weak localization. (a)–(d) Differential longitudinal conductivity $\mathrm{\Delta }{\sigma }_{xx}(T,H)\equiv {\sigma }_{xx}(T,H)-{\sigma }_{xx}(T,0)$ vs magnetic field at $1.6\text{K}$ (black dots) at (a) $V_g-V_{\text{min}}=-9\text{V}$, (b) $-5\text{V}$, (c) $-3\text{V}$, and (d) $1.5\text{V}$. The classical contribution to the magnetoconductance has been subtracted from the data [19]. The absolute conductivity at $B=0$ at each gate voltage is indicated. The HLN formula for WAL with a crossover to WL is fit to the data (red lines); the quality of the fit becomes poor when ${\sigma }_{xx}\lesssim e^2/h$.

Figure 4

Coherence lengths near the Dirac point. The characteristic coherence length $l_{\varphi }$, extracted from fitting Eq. (4) to the magnetoconductance, shown vs temperature at various gate voltages. A small range in $B$ is chosen when fitting to isolate the lowest-order contribution. $l_{\varphi }$ is fit by a power law in temperature $l_{\varphi }\propto T^{-p}$, yielding $p=0.39$, 0.37, and 0.26 at $V_g-V_{\text{min}}=-8, -6$, and $-4$ V, respectively. As $V_g$ approaches $V_{\text{min}}$, the temperature dependence of $l_{\varphi }$ flattens at low temperature.