  We present a combined experimental and theoretical study of the surface
vibrational modes of the topological insulator (TI) Bi$_2$Se$_3$ with
particular emphasis on the low-energy region below 10 meV that has been
difficult to resolve experimentally. By applying inelastic helium atom
scattering (HAS), the entire phonon dispersion was determined and compared with
density functional perturbation theory (DFPT) calculations. 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 calculations. Besides these results, the experimental data reveal$-$via
bound-state resonance enhancement$-$two additional dispersion curves in the gap
below the Rayleigh mode. They are possibly associated with an excitation of a
surface electron density superstructure that we observe in HAS diffraction
patterns. The electron-phonon coupling paramenter $\lambda$ = 0.23 derived from
our temperature dependent Debye-Waller measurements compares well with values
determined by angular resolved photoemission or Landau level spectroscopy. Our
work opens up a new perspective for THz measurements on 2D materials as well as
the investigation of subtle details (band bending, the presence of quantum well
states) with respect to the electron-phonon coupling.
