The following dissertation presents a comprehensive study of the interaction between Dirac fermion quasiparticles (DFQs) and surface phonons on the surfaces of the topological insulators Bi2Se3 and Bi2Te3. Inelastic helium atom surface scattering (HASS) spectroscopy and time of flight (TOF) techniques were used to measure the surface phonon dispersion of these materials along the two high-symmetry directions of the surface Brillouin zone (SBZ). Two anomalies common to both materials are exhibited in the experimental data. First, there is an absence of Rayleigh acoustic waves on the surface of these materials, pointing to weak coupling between the surface charge density and the surface acoustic phonon modes and potential applications for soundproofing technologies. Secondly, both materials exhibit an out-of-plane polarized optical phonon mode beginning at the SBZ center and dispersing to lower energy with increasing wave vector along both high-symmetry directions of the SBZ. This trend terminates in a V-shaped minimum at a wave vector corresponding to 2kF for each material, after which the dispersion resumes its upward trend. This phenomenon constitutes a strong Kohn anomaly and can be attributed to the interaction between the surface phonons and DFQs. To quantify the coupling between the optical phonons experiencing strong renormalization and the DFQs at the surface, a phenomenological model was constructed based within the random phase approximation. Fitting the theoretical model to the experimental data allowed for the extraction of the matrix elements of the coupling Hamiltonian and the modifications to the surface phonon propagator encoded in the phonon self energy. This allowed, for the first time, calculation of phonon mode-specific quasiparticle-phonon coupling λⱱ(q) from experimental data. Additionally, an averaged coupling parameter was determined for both materials yielding ¯λ^Te ≈ 2 and ¯λ^Se ≈ 0.7. These values are significantly higher than those of typical metals, underscoring the strong coupling between optical surface phonons and DFQs in topological insulators. In an effort to connect experimental results obtained from phonon and photoemission spectroscopies, a computational process for taking coupling information from the phonon perspective and translating it to the DFQ perspective was derived. The procedure involves using information obtained from HASS measurements (namely the coupling matrix elements and optical phonon dispersion) as input to a Matsubara Green function formalism, from which one can obtain the real and imaginary parts of the DFQ self energy. With these at hand it is possible to calculate the DFQ spectral function and density of states, allowing for comparison with photoemission and scanning tunneling spectroscopies. The results set the necessary energy resolution and extraction methodology for calculating ¯λ from the DFQ perspective. Additionally, determining ¯λ from the calculated spectral functions yields results identical to those obtained from HASS, proving the self-consistency of the approach.

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