Contrasting the Surface Phonon Dispersion of Pb_{0.7}Sn_{0.3}Se in Its Topologically Trivial and Nontrivial Phases.

We report inelastic He atom scattering measurements of the (001) surface phonon dispersion of the topological crystalline insulator Pb_{0.7}Sn_{0.3}Se. This material exhibits a temperature-dependent topological transition, so we measure the surface dispersion curves in both the trivial and nontrivial phases. We identify that, peculiarly, most surface modes are resonances, rather than pure surface states. We find that a shear vertical surface resonance branch around 9.0 meV dramatically changes on going from the trivial to the topological phase. We associate this remarkable change with the emergence of surface Dirac fermions. We use the measured dispersion of this resonance branch to determine the corresponding mode-dependent electron-phonon coupling λ_{ν}(q).