Measuring, Interpreting and Translating Electron Quasiparticle - Phonon Interactions on the Surfaces of the Topological Insulators Bismuth Selenide and Bismuth Telluride

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The thesis presents experimental and theoretical findings on the surface dynamics and surface Dirac fermion (DF) spectral function of strong topological insulators Bi2Te3 and Bi2Se3. Experimental results indicate a strong Kohn anomaly in the surface phonon dispersion of a low-lying optical mode, alongside the absence of surface Rayleigh acoustic phonons. By fitting the experimental data to theoretical models using phonon Matsubara functions, the study extracted matrix elements of the coupling Hamiltonian and modifications to the surface phonon propagator encoded in the phonon self-energy. This enabled the first calculation of phonon mode-specific DF coupling λ ν (q) from experimental data, revealing an average coupling significantly higher than typical values for metals, highlighting the strong coupling between optical surface phonons and surface DFs in topological insulators. To correlate with experimental results from photoemission spectroscopies, an electronic (DF) Matsubara function was constructed using the determined electron-phonon matrix elements and optical phonon dispersion. This facilitated the calculation of the DF spectral function and density of states, allowing for comparisons with photoemission and scanning tunneling spectroscopies. The findings establish the necessary energy resolution and extraction methodology for calculating λ from the DF perspective.