Quasiparticle - phonon coupling on the surface of the family of topological crystalline insulators Pb1-xSnxSe

We report on studies of the interaction between Dirac fermion quasiparticles (DFQs) and surface phonons in the family Pb1_-xSn_xSe using inelastic helium atom scattering. In particular, we examine the phonon dispersion along the Γ- X line of the surface Brillouin zone, which contains a mirror plane whose existence gives rise to topologically protected DFQs as manifest in two Dirac cones straddling the X point. Anomalies in the phonon dispersion curves are studied as the system goes through a Lifshitz transition, and results indicate that both intra and inter-cone electron scattering play a major role in renormalizing the phonon energies. Fitting the obtained phonon dispersions to a phenomenological model allows us to determine the corresponding electron-phonon matrix elements. These are then used in conjunction with a Matsubara Green function formalism to obtain the real and imaginary parts of the electron self energy and ultimately the quasiparticle spectral function. In doing so we translate the information from our phonon spectra to the electron perspective, allowing us to highlight potentially interesting surface Brillouin zone regions for study in future electron spectroscopy experiments.