Fermi level tuning and a large activation gap achieved in the topological insulator Bi${}_2$Te${}_2$Se by Sn doping

We report the effect of Sn doping on the transport properties of the topological insulator Bi${}_2$Te${}_2$Se studied in a series of Bi${}_{2-x}$Sn${}_x$Te${}_2$Se crystals with 0 $\le$ $x$ $\le$ 0.02. The undoped stoichiometric compound ($x$ $=$ 0) shows an $n$-type metallic behavior with its Fermi level pinned to the conduction band. In the doped compound, it is found that Sn acts as an acceptor and leads to a downshift of the Fermi level. For $x$ $\ge$ 0.004, the Fermi level is lowered into the bulk forbidden gap and the crystals present a resistivity considerably larger than 1 $\Omega$ cm at low temperatures. In those crystals, the high-temperature transport properties are essentially governed by thermally activated carriers whose activation energy is 95–125 meV, which probably signifies the formation of a Sn-related impurity band. In addition, the surface conductance directly obtained from the Shubnikov–de Haas oscillations indicates that a surface-dominated transport can be achieved in samples with several $\mu$m thickness.

Figure 1

(a) Temperature dependencies of ${\rho }_{xx}$ for Bi${}_{2-x}$Sn${}_x$Te${}_2$Se single-crystal samples with various $x$. Note that the data with $x$ $=$ 0 and $x$ $=$ 0.002 have been magnified by a factor of 500 and 10, respectively. For comparison, the data for an insulating sample grown from the starting composition Bi${}_2$Te${}_{1.95}$Se${}_{1.05}$ are also included (dashed line). (b) Arrhenius plot of the ${\rho }_{xx}\left(T\right)$ data for the temperature range between 100 and 300 K. (c) ${\rho }_{xx}\left(T\right)$ data for four representative samples with $x$ $=$ 0.006 obtained from different parts of a boule. The data are labeled in numerical order, where S1 and S4 represent first-to-freeze and the end parts, respectively. Note that the vertical axis is in logarithmic scale.

Figure 2

(a) Temperature dependencies of the low-field Hall coefficient $R_{\mathrm{H}}$ for a series of Bi${}_{2-x}$Sn${}_x$Te${}_2$Se samples, together with the data for the BTS${}_{1.05}$ sample. The inset shows a magnified view of the data with $x$ $=$ 0 and $x$ $=$ 0.002. (b) Arrhenius plot of $R_{\mathrm{H}}\left(T\right)$ at high temperature for a series of samples except for $x$ $=$ 0 and 0.002 where no activation behavior was observed. Dashed lines are the Arrhenius-law fittings to extract the activation energy ${\Delta }^{*}$. (c) $R_{\mathrm{H}}\left(T\right)$ data for two different samples with $x$ $=$ 0.004, showing both $n$-type and $p$-type behavior. (d) The density of introduced holes [$\Delta n_h=n\left(x\right)-n\left(0\right)$] by Sn doping plotted as a function of the density of Sn dopant atoms. The estimation of the carrier density is based on a one-band model for simplicity. The dashed line corresponds to the ideal situation where each Sn atom donates one hole.

Figure 3

(a) Transverse conductance $G_{yx}$ for an $n$-type sample with $x$ $=$ 0.004 at 1.6 K plotted as a function of magnetic field $B$ applied along the $C_3$ axis. The inset shows the oscillatory component of $G_{yx}$, $\Delta$$G_{yx}$, plotted as a function of 1/$B$. The dashed lines are a guide to the eyes. (b) Landau-level fan diagram for oscillations in $\Delta$$G_{yx}$. Maxima and minima correspond to $n+1/4$ and $n+3/4$, respectively. The linear fitting with the slope of $F$ $=$ 116 T fixed by the oscillation frequency intersects the axis at $\beta$ $=$ 0.4 $\pm$ 0.1. (c) Dingle plot for the oscillations in $\Delta$$R_{xx}$, yielding $T_D$ $=$ 12.5 K; inset shows the temperature dependence of the SdH amplitudes. The solid line represents the fitting by the LK theory, giving $m_c$ $=$ 0.13$m_e$.

Figure 4

$G_{yx}$ for a sample with $x$ $=$ 0.01 at 1.6 K plotted as a function of $B$ applied along the $C_3$ axis. The upper inset shows the oscillatory component $\Delta$$G_{yx}$ plotted as a function of $1/B$. The lower inset shows the Fourier transform of $\Delta G_{yx}\left(B^{-1}\right)$, revealing two prominent frequencies.