Electron-phonon coupling and surface Debye temperature of ${\mathbf{Bi}}_2{\mathbf{Te}}_3$(111) from helium atom scattering

We have studied the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) by means of helium atom scattering. The average electron-phonon coupling $\lambda$ of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) is determined by adapting a recently developed quantum-theoretical derivation of the helium scattering probabilities to the case of degenerate semiconductors. Based on the Debye-Waller attenuation of the elastic diffraction peaks of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111), measured at surface temperatures between 110 and $355\text{K}$, we find $\lambda$ to be in the range of $0.04\text{–}0.11$. This method allows us to extract a correctly averaged $\lambda$ and to address the discrepancy between previous studies. The relatively modest value of $\lambda$ is not surprising even though some individual phonons may provide a larger electron-phonon interaction. Furthermore, the surface Debye temperature of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) is determined as ${\mathrm{\Theta }}_D=(81\pm 6)\text{K}$. The electronic surface corrugation was analyzed based on close-coupling calculations. By using a corrugated Morse potential a peak-to-peak corrugation of 9% of the lattice constant is obtained.

Figure 1

Scattered He intensities (logarithmic scale) for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) vs incident angle ${\vartheta }_i$ for the two high-symmetry directions. The upper panel shows a scan along the $\overline{\mathrm{\Gamma }\mathrm{M}}$ azimuth and the lower panel shows a scan along $\overline{\mathrm{\Gamma }\mathrm{K}}$. The upper abscissa shows the corresponding parallel momentum transfer. In both cases the crystal was kept at 110 K and an incident beam energy of 8 meV was used. The inset in the upper panel shows the surface Brillouin zone and the scanning directions. The red squares show the peak areas determined from measurements (scaled relative to the specular intensity). They are in good agreement with best-fit results from close-coupling calculations (green crosses), except for a slight asymmetry in the angular scan along $\overline{\mathrm{\Gamma }\mathrm{M}}$. The inset in the lower panel shows a contour plot of the surface corrugation as obtained by the best-fit results from the close-coupling calculation.

Figure 2

Decay of the logarithmic specular peak intensity $ln\left[I\left(T_S\right)\right]$ vs surface temperature $T_S$ using an incident-beam energy of 8 meV for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111).

Figure 3

Decay of the logarithmic peak intensity $ln\left[I\left(T_S\right)\right]$ with increasing surface temperature $T_S$ of the first-order diffraction peak along $\overline{\mathrm{\Gamma }\mathrm{M}}$ measured at an incident-beam energy of 8 meV. In the inset, angular scans over the peak are depicted for a selection of different temperatures.

Figure 4

Photoemission intensity for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) along $\overline{\mathrm{\Gamma }\mathrm{M}}$ of (a) the sample of the present HAS study and (b) the sample measured by Michiardi et al. (adapted figure with permission from [21], Copyrighted by the American Physical Society) at three different values of the normal momentum transfer (with the zero conventionally set at the $\overline{\mathrm{\Gamma }}$ point). The positions of the Fermi level (F), the conduction-band minimum (CBm), the valence-band maximum (VBM), and the Dirac point (D) are indicated by the horizontal lines. The dashed red lines show the quasilinear dispersion of the surface Dirac states.