Strong surface scattering in ultrahigh-mobility ${\text{Bi}}_2{\text{Se}}_3$ topological insulator crystals

While evidence of a topologically nontrivial surface state has been identified in surface-sensitive measurements of ${\text{Bi}}_2{\text{Se}}_3$, a significant experimental concern is that no signatures have been observed in bulk transport. In a search for such states, nominally undoped single crystals of ${\text{Bi}}_2{\text{Se}}_3$ with carrier densities approaching ${10}^{16}{\text{cm}}^{-3}$ and very high mobilities exceeding $2{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$ have been studied. A comprehensive analysis of Shubnikov-de Haas oscillations, Hall effect, and optical reflectivity indicates that the measured electrical transport can be attributed solely to bulk states, even at 50 mK at low Landau-level filling factor, and in the quantum limit. The absence of a significant surface contribution to bulk conduction demonstrates that even in very clean samples, the surface mobility is lower than that of the bulk, despite its topological protection.

Figure 1

(Color online) (a) Comparison of the electrical resistivity $\rho \left(T\right)$ between samples of ${\text{Bi}}_2{\text{Se}}_3$. Carrier densities $n\left({\text{cm}}^{-3}\right)$ are estimated from SdH oscillations: (i) $1\times {10}^{19}$, (ii) $5.3\times {10}^{18}$, (iii) $4.9\times {10}^{17}$, (iv) $3.7\times {10}^{17}$, (v) $3.3\times {10}^{17}$, and (vi) $\sim {10}^{16}$. In samples with $n<{10}^{18}{\text{cm}}^{-3}$, a shallow minimum develops at 30 K. (b) Comparison of Hall carrier density $n_{\text{H}}$ between various samples. Low-temperature values span 3 orders of magnitude.

Figure 2

(Color online) (a) A comparison of electrical resistivity $\rho \left(T\right)$ (iii from Fig. 1) and Hall carrier density $n_{\text{H}}\left(T\right)$ in two samples from the same batch. The minimum in $\rho \left(T\right)$ coincides with the saturation of $n_{\text{H}}\left(T\right)$ below 30 K. Despite increasing $n_{\text{H}}$, $\rho$ increases with $T$ up to 300 K. (b) The calculated mobility exceeds $2{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$ at low $T$ (labeled ${10}^{17}$). The mobilities of samples with lower and higher $n$ are compared. (c) Field orientation dependence of $\rho$ at 1.8 K. Compare to $\rho \left(H\right)$ of sample vi (rescaled by factor of 10), which exhibits no SdH oscillations.

Figure 3

(Color online) Temperature dependence of SdH oscillations with (a) $H\parallel c_3$ trigonal axis and (b) $H\perp c_3$. Oscillation frequencies $f_{\text{SdH}}=20\text{T}$ and 25 T, respectively, and the mass $m_{\text{SdH}}\approx 0.15m_{\text{e}}$. SdH oscillations from two different samples at 50 mK in the (c) transverse and (d) longitudinal MR. The largest amplitude and smallest frequency in (c) is observed with $H\parallel c_3$ and the frequency ranges from 20 to 27 T. In (d) the largest amplitude is observed with $H\perp c_3$ and $f_{\text{SdH}}=15\text{T}$. Only one SdH frequency is observed in each measurement.

Figure 4

(Color online) Spectra of (a) reflectivity, (b) optical conductivity, and (c) dielectric constant. Curves (b) and (c) were calculated from the fit to the reflectivity data in (a). For comparison, the (blue) circle and (red) square in (b) are dc values from sample iv for 6 K and room temperature, respectively.