Contrasting the Surface Phonon Dispersion of the Topological Crystalline Insulator Pb_0.7Sn_0.3Se in its Topologically Trivial and Nontrivial Phases

We report inelastic He atom surface-scattering measurements of the (001) surface phonons dispersion of the topological crystalline insulator Pb_0.7Sn_0.3Se. Because this material exhibits a temperature-dependent topological transition, we measure the surface dispersion curves in both the trivial and topological phases. Peculiarly, most surface phonon modes appear as resonances, rather than pure surface states. We find that a vertical shear surface resonance branch around 1.9 THz dramatically changes on going from the trivial to the topological phase. We associate this remarkable change with a strong interaction of the emergent surface Dirac fermions with the modes of this branch. We use the measured dispersion of this resonance branch to determine the corresponding mode-dependent electron-phonon coupling λ_ν(q).