Manifestation of Topological Protection in Transport Properties of Epitaxial ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ Thin Films

The massless Dirac fermions residing on the surface of three-dimensional topological insulators are protected from backscattering and cannot be localized by disorder, but such protection can be lifted in ultrathin films when the three-dimensionality is lost. By measuring the Shubnikov–de Haas oscillations in a series of high-quality ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films, we revealed a systematic evolution of the surface conductance as a function of thickness and found a striking manifestation of the topological protection: The metallic surface transport abruptly diminishes below the critical thickness of $\sim 6\mathrm{nm}$, at which an energy gap opens in the surface state and the Dirac fermions become massive. At the same time, the weak antilocalization behavior is found to weaken in the gapped phase due to the loss of $\pi$ Berry phase.

Figure 1

(a) AFM image of a 50-nm thick ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film showing atomically flat terraces with 1-QL steps. Inset: typical RHEED pattern. (b) X-ray diffraction pattern of a 200-QL film. (c) Temperature dependences of $R_s$ for different thickness.

Figure 2

Surface SdH oscillations in the 10-QL film. (a) $d{R}_{yx}/dB$ in tilted magnetic fields, plotted as a function of $1/B_{\perp }$ ($=1/B\cos \theta$); curves are shifted vertically for clarity. Dashed lines mark the positions of maxima. Inset shows the geometry of the experiment. (b) Dingle plot of the oscillations in $\Delta R_{xx}$ at 1.6 K, obtained after subtracting a smooth background from $R_{xx}(B)$, giving the Dingle temperature of 16 K. Inset: $T$-dependence of the SdH amplitude for $\theta =0°$. (c) Landau-level fan diagram for oscillations in $G_{xx}$ measured at $T=1.6\mathrm{K}$ and $\theta =0°$; following Ref. 43, integers $n$ (half-integers $n+\frac{1}{2}$) are assigned to the minima (maxima) in $\Delta G_{xx}$. The solid line is a linear fitting to the data with the slope fixed at $F=106.8\mathrm{T}$; the dashed line has the same slope and extrapolates to zero. Upper inset shows $\Delta G_{xx}$ vs $1/B$ after subtracting a smooth background; lower inset shows its Fourier transform giving $F=106.8\mathrm{T}$. (d) Fitting of the two-band model to the $R_{yx}(B)$ data at 1.6 K.

Figure 3

(a) Squares are the $n_s$ obtained from SdH oscillations (open and filled squares represent two different surfaces of the same film) and the dashed squares are an extrapolation of the trend above $t_c$; circles are the sheet density of bulk carriers obtained from two-band analyses. (b) Mobilities of surface (squares) and bulk (circles) carriers obtained from two-band analyses. (c) $G_s/G_{\mathrm{tot}}$ obtained from the data in (a) and (b). Insets are schematic pictures of the energy bands for the two regimes. (d) $R_{yx}(B)$ at 1.6 K for various thickness shown in QL unit; inset shows the derivative $d{R}_{yx}/dB$ for the 5 and 8 QL films (5-QL data are shifted for clarity). (e) $R_{xx}(B)/R_{xx}(0)$ of the same films.

Figure 4

(a) WAL behavior in sheet conductance at 1.6 K for various thicknesses shown in QL units; dashed lines are the fittings using Eq. (1). (b) Thickness dependence of $\alpha$. Inset shows schematic energy bands above and below the critical thickness.