Observations of two-dimensional quantum oscillations and ambipolar transport in the topological insulator Bi${}_2$Se${}_3$ achieved by Cd doping

We present a defect-engineering strategy to optimize the transport properties of the topological insulator Bi${}_2$Se${}_3$ to show a high bulk resistivity and clear quantum oscillations. Starting with a $p$-type Bi${}_2$Se${}_3$ obtained by combining Cd doping and a Se-rich crystal-growth condition, we were able to observe a $p$-to-$n$-type conversion upon gradually increasing the Se vacancies by post annealing. With the optimal annealing condition, where a high level of compensation is achieved, the resistivity exceeds 0.5 $\Omega$cm at 1.8 K and we observed two-dimensional Shubnikov–de Haas oscillations composed of multiple frequencies in magnetic fields below 14 T.

Figure 1

(a) Temperature dependences of ${\rho }_{xx}$ of an as-grown Bi${}_{1.998}$Cd${}_{0.002}$Se${}_3$ crystal (solid line) and a pristine Bi${}_2$Se${}_3$ crystal (dashed-dotted line) grown in the same Se-rich condition. The pristine sample is $n$ type with $n_{\mathrm{e}}\sim$$7\times 10$${}^{17}$ cm${}^{-3}$, while the Cd-doped sample is $p$ type with $n_{\mathrm{h}}\sim$ $9\times 10$${}^{18}$ cm${}^{-3}$. Note that the low-temperature resistivity upturn in the pristine sample is absent in the Cd-doped sample. (b) Temperature dependences of $R_{\mathrm{H}}$ (left axis) and ${\mu }_{\mathrm{H}}$ (right axis) for the Cd-doped sample; inset shows the magnetic field dependence of ${\rho }_{yx}$ in this sample at 1.8 K.

Figure 2

(a) Temperature dependences of ${\rho }_{xx}$ for Bi${}_{1.998}$Cd${}_{0.002}$Se${}_3$ crystals annealed at different temperatures in evacuated quartz tubes. The data for the as-grown crystal are also shown for comparison. The low-temperature resistivity values span three orders of magnitude. (b) Temperature dependences of $R_H$ for the same series of samples. As the annealing temperature is increased, the crystal becomes less $p$ type and is eventually converted to $n$ type. This conversion occurs with the annealing temperature of $\sim$577 ${}^{\circ }$C.

Figure 3

(a)–(d) Reproducibility of the ${\rho }_{xx}\left(T\right)$ data in samples annealed at the same temperature, demonstrated for four different values of $T_{\mathrm{anneal}}$ indicated in each panel.

Figure 4

(a)–(d) Reproducibility of the $R_{\mathrm{H}}\left(T\right)$ data in samples annealed at the same temperature, demonstrated for four different values of $T_{\mathrm{anneal}}$ indicated in each panel. (e)–(h) Magnetic-field dependences of ${\rho }_{yx}$ measured in sample “A” of each $T_{\mathrm{anneal}}$. The solid line in (g) is the two-band-model fitting to the data.

Figure 5

(a) $R_{\mathrm{H}}\left(T\right)$ data of the sample C of $T_{\mathrm{anneal}}$ = 577 ${}^{\circ }$C after the Al${}_2$O${}_3$-coverage process. (b) ${\rho }_{yx}\left(B\right)$ data of the same sample measured at 1.4 K; the solid line is the result of the two-band-model fitting. (c) Magnetic-field dependences of the primary signal (${\rho }_{xx}$) and the second-harmonic signal ($\Delta {\rho }_{xx}$) measured at 1.4 K in magnetic fields along the $C_3$ axis. (d) Plots of $\Delta {\rho }_{xx}\left(B\right)$ and $d^2{\rho }_{xx}/d{B}^2$ vs the inverse magnetic field $1/B$. Clear SdH oscillations can be seen in both data, and good agreements in the positions of peaks and dips between the two curves are evident. (e) The FT spectrum of $\Delta {\rho }_{xx}$ show three prominent frequencies.

Figure 6

(a) The $\Delta {\rho }_{xx}$ data for varying magnetic-field directions, plotted as a function of $1/\left(B\cos \theta \right)$; dashed lines mark the positions of the peaks. (b) The three prominent frequencies in the FT spectra of the SdH oscillations plotted as a function of $\theta$. All the frequencies vary as $1/\cos \theta$, as indicated by the solid lines.