Large bulk resistivity and surface quantum oscillations in the topological insulator ${\text{Bi}}_2{\text{Te}}_2\text{Se}$

Topological insulators are predicted to present interesting surface transport phenomena but their experimental studies have been hindered by a metallic bulk conduction that overwhelms the surface transport. We show that the topological insulator ${\text{Bi}}_2{\text{Te}}_2\text{Se}$ presents a high resistivity exceeding $1\Omega \text{cm}$ and a variable-range hopping behavior, and yet presents Shubnikov-de Haas oscillations coming from the topological surface state. Furthermore, we have been able to clarify both the bulk and surface transport channels, establishing a comprehensive understanding of the transport in this material. Our results demonstrate that ${\text{Bi}}_2{\text{Te}}_2\text{Se}$ is, to our knowledge, the best material to date for studying the surface quantum transport in a topological insulator.

Figure 1

(Color online) (a) Layered crystal structure of ${\text{Bi}}_2{\text{Te}}_2\text{Se}$ showing the ordering of Te and Se atoms. (b) Comparison of the x-ray powder-diffraction patterns of ${\text{Bi}}_2{\text{Te}}_2\text{Se}$ and ${\text{Bi}}_2{\text{Te}}_3$. Arrows indicate the peaks characteristic of ${\text{Bi}}_2{\text{Te}}_2\text{Se}$. (c) Temperature dependence of ${\rho }_{xx}$ for samples 1–3; inset shows $R_H\left(T\right)$ for the same samples. (d) Plot of the conductivity ${\sigma }_{xx}\left(={\rho }_{xx}^{-1}\right)$ vs $T^{-1/4}$ for sample 1. Dashed line is the fitting of the 3D VRH behavior ${\sigma }_{xx}\sim \text{exp}\left[-{\left(T/T_0\right)}^{-1/4}\right]$ to the data; deviation from the fitting at low temperature, shown by solid line, signifies the parallel metallic conduction. Inset shows the Arrhenius plot of ${\rho }_{xx}$.

Figure 2

(Color online) (a) $d{\rho }_{yx}/dB$ vs $1/B_{\perp }\left[=1/\left(B\text{cos}\theta \right)\right]$ in magnetic fields tilted from the $C_3$ axis at different angles $\theta$, where all curves are shifted for clarity; lower inset shows the schematics of the experiment and the definition of $\theta$. Equidistant dashed lines in the main panel emphasize that the positions of maxima for any $\theta$ depends only on $B_{\perp }$; upper inset shows the $1/\text{cos}\theta$ dependence of the oscillation frequency. Both point to the 2D FS. (b) Dingle plot for the oscillations in $\Delta {\rho }_{yx}$, which is obtained after subtracting a smooth background from ${\rho }_{yx}$, giving $T_D=25.5\text{K}$; inset shows the $T$ dependence of the SdH amplitude for $\theta \simeq 0°$, yielding $m_c=0.11m_e$. (c) Landau-level fan diagram for oscillations in $d{\rho }_{xx}/dB$ measured at $T=1.6\text{K}$ and $\theta \simeq 0°$. Inset shows $d{\rho }_{xx}/dB$ vs $1/B$ after subtracting a smooth background. Minima and maxima in $d{\rho }_{xx}/dB$ correspond to $n+\frac{1}{4}$ and $n+\frac{3}{4}$, respectively. The least-square fitting intersects the axis at $n=0.22\pm 0.12$. (d) Temperature dependence of the low-field $R_H$; dotted line represents the activated behavior. Inset shows the ${\rho }_{yx}\left(B\right)$ curve at 1.6 K and its fittings with the two-band model.

Figure 3

(Color online) Schematic picture of the bulk and surface band structures (left), together with the energy diagram of the density of states of the bulk and impurity bands (right), where $E_F^s=130\text{meV}$, $\Delta \approx 30\text{meV}$, and $E_g\approx 300\text{meV}$. In the impurity band which is due to the acceptor levels and is located within the band gap, only the central part forms the extended states and the tails consist of localized states.