Experimental Demonstration of Topological Surface States Protected by Time-Reversal Symmetry

We report direct imaging of standing waves of the nontrivial surface states of topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ using a scanning tunneling microscope. The interference fringes are caused by the scattering of the topological states off Ag impurities and step edges on the ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ surface. By studying the voltage-dependent standing wave patterns, we determine the energy dispersion $E(k)$, which confirms the Dirac cone structure of the topological states. We further show that, very different from the conventional surface states, backscattering of the topological states by nonmagnetic impurities is completely suppressed. The absence of backscattering is a spectacular manifestation of the time-reversal symmetry, which offers a direct proof of the topological nature of the surface states.

Figure 1

(a) The STM topograph ($250\mathrm{nm}\times 250\mathrm{nm}$) of the ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ film. Imaging conditions: $V=3\mathrm{V}$, $I=50\mathrm{pA}$. (b) The atomic-resolution image ($-40\mathrm{mV}$, 0.1 nA). Tellurium atom spacing is about 4.3 Å. (c) $dI/dV$ spectrum taken on bare ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ surface. Set point: $V=0.3\mathrm{V}$, $I=0.1\mathrm{nA}$. The arrows indicate the bottom of conduction band (right) and the top of valence band (left), respectively. (d) Calculated band structure of ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ along high-symmetry directions of SBZ (see the inset). The lines around the $\overline{\Gamma }$ point in the energy gap are the surface states.

Figure 2

Standing waves induced by Ag trimmers on ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ surface. (a) STM image ($28\mathrm{nm}\times 28\mathrm{nm}$) of a region with four Ag trimmers adsorbed on ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ surface. (b) The adsorption geometry of Ag trimmer. (c)–(g) The $dI/dV$ maps of the same area as (a) at various sample bias voltages. The current was set at 0.1 nA. Each map has $128\times 128$ pixels and took 2 h to complete. The interference fringes are evident in the images. (h)–(k) The FFT power spectra of the $dI/dV$ maps in (c)–(g). The SBZ in (h) is superimposed on the power spectra to indicate the directions in $\overrightarrow{q}$ space. The resolution of FFT, which is $2\pi /28{\mathrm{nm}}^{-1}$, is determined by the size of the STM image.

Figure 3

(a) The scattering geometry. The CEC is in the shape of a hexagram. The dominant scattering wave vectors connect two points in $\overline{\Gamma }\mathrm{\text{−}}\overline{K}$ directions on CEC. ${\overrightarrow{k}}_i$ and ${\overrightarrow{k}}_f$ denote the wave vectors of incident and scattered states. ${\overrightarrow{q}}_1$, ${\overrightarrow{q}}_2$, and ${\overrightarrow{q}}_3$ are three possible scattering wave vectors. (b) Energy dispersion as a function of $k$ in the $\overline{\Gamma }\mathrm{\text{−}}\overline{K}$ direction. The data are derived from FFT in Fig. 2. The line shows a linear fit to the data with $v_F=4.8\times {10}^5\mathrm{m}/\mathrm{s}$. The error bars represent the resolution of FFT (see the caption of Fig. 2).

Figure 4

Standing waves on the upper terrace by a step edge [(a)–(h)]. All of the images are $dI/dV$ maps at various bias voltages of an area of $35\times 35\mathrm{nm}$. Imaging conditions: $I=0.1\mathrm{nA}$. (i) Energy dispersion deduced from the standing waves at the step edge. The dispersion is a function of the scattering wave vector $q$. The inserted STM image shows the step that produces the standing waves in (a)–(h).