Interaction between Phonons and Dirac Fermions on the  Surface of the Topological Crystalline Insulator Pb1-xSnxSe
This event is part of the Preliminary Oral Exam.
Examining Committee: Michael El-Batanouny, Claudio Chamon, Karl Ludwig, and John Butler
Topological crystalline insulators (TCIs) belong to a class of topological insulators whose surface Dirac fermion metallic states are protected by crystalline symmetry, as opposed to time-reversal symmetry. These surface states exhibit chirality and spin helicity. The material Pb1-xSnxSe, with rocksalt crystal structure, becomes a TCI above a critical Sn concentration of xc=18%. In the topological phase, Pb1-xSnxSe has a bulk band inversion around the gap at the L-point. It exhibits a rich assortment of novel phenomena including a temperature-dependent transition from the trivial to the topological phase, double Dirac cones that give rise to a prominent van Hove singularity, as well as a Lifshitz Fermi surface topology transition. Revealing the surface dynamical signatures associated with such phenomena will provide a solid basis for explaining the fundamental physics of these systems. For example, dynamical changes manifest in the Lifshitz transition will bring to light how modifications of the Fermi surface topology affect a physical system’s dynamic response. The Dirac fermion states are robust against backscattering by impurities, phonons, and defects, making TCIs promising for applications in spintronics and quantum computing. While material improvements may minimize impurities and defects, phonons are always present, which makes understanding the physics of the electron-phonon coupling in these materials especially important. I am using the technique of inelastic scattering of helium beams from surfaces to investigate changes in surface dynamics as the system undergoes the transition from the trivial to the topological phase. Special attention is given to the appearance of topological signatures in the measured surface phonon dispersions along high-symmetry directions of the  surface Brillouin zone. These signatures will be analyzed using temperature-dependent Matsubara Green’s functions to precisely determine phonon-mode-specific electron-phonon couplings λν(q). I am also using elastic He scattering to track the evolution of the surface charge density topographies through the transition.