Dr Colin Howard was awarded a PhD from Boston University in 2015.  In 2012 he received the Gertrude and Maurice Goldhaber Award for Excellence in Physics Research, awarded annually to a single graduate student at Boston University for making exceptional contributions to research in their first year of graduate study.

The thesis presents experimental and theoretical results about the surface dynamics and the surface Dirac fermion (DF) spectral function of the strong topological insulators Bi2Te3 and Bi2Se3. The experimental results reveal the presence of a strong Kohn anomaly in the measured surface phonon dispersion of a low-lying optical mode, and the absence of surface Rayleigh acoustic phonons. Fitting the experimental data to theoretical models employing phonon Matsubara functions allowed the extraction of the matrix elements of the coupling Hamiltonian and the modifications to the surface phonon propagator that are encoded in the phonon self-energy. This allowed, for the first time, calculation of phonon mode-specific DF coupling ¿_¿(q) from experimental data, with average coupling significantly higher than typical values for metals, underscoring the strong coupling between optical surface phonons and surface DFs in topological insulators. Finally, to connect to experimental results obtained from photoemission spectroscopies, an electronic (DF) Matsubara function was constructed using the determined electron-phonon matrix elements and the optical phonon dispersion. This allowed calculation of the DF 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 ¿ from the DF perspective.

1 Introduction 2 Properties of Bi2Se3 and Bi2Te3 2.1 Crystal structure 2.2 Bulk vibrational structure 2.3 Electronic structure 3 Helium atom-surface scattering (HASS) 3.1 The benefits of HASS 3.2 The surface interaction potential 3.3 The kinematics of HASS 3.3.1 Elastic scattering 3.3.2 Inelastic scattering and time-of-flight technique 4 Experimental Apparatus and Technique 4.1 Surface Laboratory facilities 4.2 Source chamber 4.3 Target chamber 4.3.1 Production and monitoring of UHV 4.3.2 Sample manipulator 4.3.3 Sample cleaver 4.3.4 Helium detector 5 Pseudocharge phonon model 5.1 Fundamentals of the model <5.2 Adiabatic approximation, ionic self-terms, and PC self-terms 5.3 Bulk parameters 5.4 Surface parameters 6 HASS results from the surface of Bi2Se3 and Bi2Te3 6.1 Elastic and inelastic scattering results 6.2 Calculation of EPC parameter in the Random Phase Approximation 7 Translating between electron and phonon perspectives 7.1 Motivation 7.2 DFQ Self Energy Formalism 7.3 Computational Results 7.4 Additional Supporting Results 8 Conclusion and future directions 8.1 Summary 8.2 Future work Appendices A Supplemental material for electron self-energy analysis A.1 Electron Green's function A.2 Bosonic sums B Numerical evaluation of the DFQ self energy B.1 Hole term B.1.1 Above Dirac point B.1.2 Below Dirac point B.2 Particle term B.2.1 Above Dirac point B.2.2 Below Dirac point B.3 Interband transitions Bibliography Curriculum Vitae