THz Surface Modes and Electron-Phonon Coupling in Bi$_2$Se$_3$(111)

We present a study of the surface vibrational modes of the topological insulator (TI) Bi$_2$Se$_3$ using inelastic helium atom scattering (HAS) as well as density functional perturbation theory (DFPT). HAS is used to determine the surface phonon dispersion curves of Bi$_2$Se$_3$(111) along the symmetry directions all over the phonon spectrum. In particular the low energy region ($<$ 10 meV) of surface phonon modes on TI surfaces is difficult to resolve experimentally and a determination of the entire phonon dispersion in this energy region is still missing for Bi$_2$Se$_3$(111). The intensity of the phonon modes is dominated by a strong Rayleigh mode, in contrast to previous experimental works. Moreover, also at variance with recent reports, no Kohn-anomaly is observed. These observations are in excellent agreement with DFPT calculation. Besides providing the surface phonon dispersion curves, the experimental data reveal via bound-state resonance enhancement, two additional dispersion curves in the gap below Rayleigh waves, possibly associated with the surface electron density superstructure observed in HAS diffraction patterns. The electron-phonon coupling $\lambda = 0.23$ derived from HAS Debye-Waller factor temperature-dependence compares well with other experimental and theoretical values obtained in presence of surface quantum well electronic states.