Observation of Huge Surface Hole Mobility in the Topological Insulator ${\mathrm{Bi}}_{0.91}{\mathrm{Sb}}_{0.09}$ (111)

We report the first direct measurement of transport properties of surface states in the topological insulator ${\mathrm{Bi}}_{0.91}{\mathrm{Sb}}_{0.09}$ (111) from the weak-field Hall effect and Shubnikov–de Haas oscillations. We find that the holelike surface band displays an unexpectedly high mobility $23000–85000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$, which is the highest mobility so far reported in bismuth-based topological insulators. This result provides the first quantitative assessment of the effect of alloy disorder on the mobility of surface states in topological insulators. We show that the 9% alloy disorder decreases the mobility of surface states by a factor of less than 2.3.

Figure 1

(a) Sketch of the (111) surface Brillouin zone with a hexagonal electron pocket around $\overline{\Gamma }$, six tear-shaped hole pockets along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction, and six bowtie-shaped electron pockets around $\overline{M}$. The $\overline{\Gamma }$, $\overline{M}$, and $\overline{K}$ are high symmetry points. (b) Surface band structure along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction mapped by ARPES experiments in ${\mathrm{Bi}}_{0.91}{\mathrm{Sb}}_{0.09}$ (111) (traced from 8, 9). The spin direction of each band is marked by the arrows. (c) The resistivity ${\rho }_{xx}$ vs temperature $T$ for samples $S1–S6$ between 4 and 200 K. The left panel of the insets shows the Arrhenius plot of $\ln {\rho }_{xx}$ vs $1/T$ for the $n$-type sample $S3$ and $p$-type sample $S6$. The right panel shows the Hall coefficient $R_H$ vs $T$ for representative $n$- and $p$-type samples.

Figure 2

(a)–(d) The Hall conductivity ${\sigma }_{xy}$ vs $H$ for samples $S5$, $S3$, $S4$, and $S1$ (red circles). The solid line is the fit to ${\sigma }_{xy}$ in Eq. (1). Arrows indicate the peak field $B_p$, which is related to the mobility by ${\mu }_{sp}=1/B_p$. (e) The conductivity ${\sigma }_{xx}$ measured with $H$ at 0.3 K for sample $S1$ (red circles). The solid curve is the calculated ${\sigma }_{xx}$ from Eq. (1) with a bulk mobility ${\mu }_b=13000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$. (f) The holelike surface Hall conductivity ${\sigma }_{xy}^{sp}$ vs $H$, obtained by subtracting the bulk term ${\sigma }_{xy}^b$ and electronlike surface Hall conductivity ${\sigma }_{xy}^{sn}$ at $T=0.3\mathrm{K}$ for sample $S1$. The solid curve is the fit to Eq. (2).

Figure 3

(a) The trace of the Hall resistivity ${\rho }_{yx}$ vs $H$ in sample $S1$ measured at temperature $T$ between 0.3 and 30 K. The inset shows that the amplitude of the weak-field Hall anomaly decreases rapidly as $T$ is raised from 0.3 to 21 K. (b) $\Delta R_{yx}$ vs $1/H$ obtained by subtracting a smooth background at selected $T$ in sample $S3$. (c) The resistivity derivative $d{\rho }_{xx}/dH$ vs $1/H_{\perp }$ with $H_{\perp }=H\cos \theta$ at selected tilt angles $\theta$ in sample $S3$. (d) The Hall resistivity derivative $d{\rho }_{yx}/dH$ vs $1/H_{\perp }$ at various $\theta$ in sample $S1$.

Figure 4

(a) ${\rho }_{xx}$ and ${\rho }_{yx}$ vs $H$ in sample $S3$ at 0.3 K. (b) The high-field quantum oscillations in the plot of $d{\rho }_{xx}/dH$ and $d{\rho }_{yx}/dH$ vs $1/H$. Black and red dashed lines correspond to the minima and maxima of $d{\rho }_{yx}/dH$, which are phase shifted by $\pi /2$ from the extrema of $d{\rho }_{xx}/dH$. (c) The Landau level index plot using the extrema of $d{\rho }_{xx}/dH$ and $d{\rho }_{yx}/dH$. The minima of $d{\rho }_{yx}/dH$ identify the fields corresponding to the filling factor $\nu$, while the minima of $d{\rho }_{yx}/dH$ correspond to $\nu -\frac{1}{4}$ [23]. (d) The normalized Hall conductivity amplitude $\Delta {\sigma }_{xy}(H)/\Delta {\sigma }_{xy}(0)$ vs $T$ at 0.3 K with 15 T. The fit to the Lifshitz-Kosevich expression gives $m_{cyc}=0.35m_e$. The inset shows the spin texture with arrows pointing to the spin direction, as revealed by ARPES measurements.