Connecting electron and phonon spectroscopies to consistently determine quasi-particle -- phonon coupling on the surface of topological insulators

Photoemission and phonon spectroscopies have yielded widely varying estimates of the electron-phonon coupling parameter on the surfaces of topological insulators, even for a particular material and technique. We connect the results of these experiments by deter- mining the Dirac fermion quasiparticle spectral function using information from measured spectra of a strongly-interacting, low-lying optical surface phonon band. The manifest spectral features resulting from the coupling are found to vary on energy scales $<$ 1 meV, and are distinct from those traditionally observed in the case of acoustic phonons in met- als. We explore different means of determining $\lambda$ from the electron perspective and identify definitions that yield values consistent with phonon spectroscopy.