Observation of Dirac Holes and Electrons in a Topological Insulator

We show that in the new topological-insulator compound ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ one can achieve a surfaced-dominated transport where the surface channel contributes up to 70% of the total conductance. Furthermore, it was found that in this material the transport properties sharply reflect the time dependence of the surface chemical potential, presenting a sign change in the Hall coefficient with time. We demonstrate that such an evolution makes us observe both Dirac holes and electrons on the surface, which allows us to reconstruct the surface band dispersion across the Dirac point.

Figure 1

(a) Basic structure unit of ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ (BSTS). (b) X-ray powder diffraction patterns of BSTS, ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$, and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Dashed lines indicate the positions of the peaks characteristic of the ordering of Se and Te ($\mathrm{Te}/\mathrm{Se}$) layers. (c) $T$ dependence of ${\rho }_{xx}$ measured repeatedly in time in a cleaved 30-$\mu \mathrm{m}$-thick BSTS sample. (d) $T$ dependence of the low-field $R_H$, presenting a sign change with time. The dashed line represents the Arrhenius-law fitting to the data above 150 K, which is also shown in the inset.

Figure 2

(a),(b) $\frac{d{\rho }_{xx}}{dB}$ vs $B_{\perp }^{-1}$ measured in tilted magnetic fields in the $p$ (5 h) and $n$ (730 h) states. All curves are shifted for clarity. Insets show the Fourier transforms of the data at $\theta =0°$. (c),(d) $T$ dependences of SdH amplitudes for $\theta =0°$ shown in (a) and (b) and their theoretical fittings; insets show $\Delta R_{xx}$ vs $B^{-1}$ after subtracting a smooth background. (e) Landau-level fan diagram obtained from the oscillations in $\Delta R_{xx}$ at 1.5 K and $\theta =0°$; minima and maxima in $\Delta R_{xx}$ correspond to $n_{\mathrm{osc}}$ and $n_{\mathrm{osc}}+\frac{1}{2}$, respectively.

Figure 3

(a),(b) Schematic picture of the bulk and surface states and the surface band bending for the $p$ and $n$ states, respectively. $E_C$ ($E_V$) is the conduction-band bottom (valence-band top); shaded band depicts the impurity band. (c) ${\rho }_{yx}(B)$ data at 1.5 K in the $p$ and $n$ states. The dashed (solid) line is the fitting of ${\rho }_{yx}(B)$ in the $n$ state ($p$ state) using the two-band (three-band) model. (d) Decomposition of the three-band ${\rho }_{yx}(B)$ fitting in the $p$ state (see text).

Figure 4

${\rho }_{xx}(T)$ data of a BSTS sample in 0 T before and after reducing its thickness. Upper inset: plot of $R_{xx}(T)$ for the same data set. Lower inset: high-$T$ activation behavior in $R_H(T)$ for the 8-$\mu \mathrm{m}$ sample, compared with that in the first sample [Fig. 1d, inset] shown as a dashed line.