STM Imaging of Electronic Waves on the Surface of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$: Topologically Protected Surface States and Hexagonal Warping Effects

Scanning tunneling spectroscopy studies on high-quality ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ crystals exhibit perfect correspondence to angle-resolved photoemission spectroscopy data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear, dispersing with a wave vector that may result from a hexagonal warping term.

Figure 1

DOS of Sn-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. (a) Crystal structure showing three quintuple units. (b) ARPES-measured Constant-energy contours of the SSB. Strength of DOS grows from blue (no DOS) to dark red (strong contribution to DOS). Note that the edge of the hexagonal Brillouin zone in the $\Gamma \mathrm{\text{−}}M$ direction is at $\sim 0.8{\AA }^{-1}$. Arrows point to the position of maximum in DOS (note sixfold symmetry). (c) Integrated DOS from ARPES. Here: $E_F$ is the Fermi level; $E_A$ is the bottom of the BCB; $E_B$ is the point of the “opening up” of the SSB; $E_C$ is the top of the BVB; and $E_D$ is the Dirac point. (d) Typical STS spectrum of a 0.27% Sn-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ sample similar to (c). Note the shift of all energies by $\sim 40\mathrm{meV}$ as a result of doping.

Figure 2

(a) Topography of the step. The total height of the step $\sim 30\AA$ corresponding to one unit cell. The height of region II is $\sim 20\AA$. Also shown is 100-fold higher resolution topograph of region III where oscillations have been studied. (b) Example of (raw data) oscillations at constant energy ($+200\mathrm{meV}$) across the width of the step. (c) Averaged spectroscopy as a function of distance from the step. The position of the step corresponds to “0” of the $x$ axis. Note the abrupt termination of the LDOS oscillations at $E_B$. (Visible features near $E_F$ are due to convolution with the electronic spectrum of the tip arising from its sharp geometry).

Figure 3

Averaged LDOS as a function of distance from the step for 8 energies. Red lines are fits to the data (see text). (a)–(e) correspond to energies above $E_B$ showing pronounced oscillations. (f)–(h) correspond to energies within the SSB, for which (h) may also reflect substantial influence of the BVB.

Figure 4

Results of fits of oscillations (see text for details) for a Cd-doped sample with Dirac point at $\sim -275\mathrm{meV}$. (a) Variation of oscillations amplitude. (b) Oscillation wave vectors (full circles) and phase shifts (open circles). Triangles follow $k_{\Gamma \mathrm{\text{−}}M}$ and $k_{\Gamma \mathrm{\text{−}}K}$, and diamonds follow $k_{\mathrm{nest}}$, all three are extracted from ARPES data of an undoped sample (see inset, for example). Arrows point to the respective Dirac points.