  We analyze the role of a Rayleigh surface phonon mode in the electron-phonon
interaction at the surface of a 3D topological insulator. A strong
renormalization of the phonon dispersion, leading eventually to the
disappearance of Rayleigh phonons, is ruled out in the ideal case of a
continuum long-wavelength limit, which is only justified if the surface is
clean and defect free. The absence of backscattering for Dirac electrons at the
Fermi surface is partly responsible for the reduced influence of the
electron-phonon interaction. A pole in the dielectric response function due to
the Rayleigh phonon dispersion could drive the electron-electron interaction
attractive at low frequencies. However, the average pairing interaction within
the weak coupling approach is found to be too small to induce a surface
superconducting instability.
