Interaction of phonons and dirac fermions on the (001) surface of the topological crystalline insulator lead tin selenide
Kalish, Samuel Abraham
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The following dissertation presents a study of the interaction between Dirac fermions and surface phonons at the (001) surface of the topological crystalline insulator Pb0.7Sn0.3Se. Nontrivial topological crystalline insulator phases are protected by an element or elements of their crystal symmetries and not by time-reversal symmetry as is the case of topological insulators. Both material types support robust metallic surface states while maintaining their bulk insulating character. Pb1-xSnxSe exhibits a temperature-dependent topological transition and thus allows the application of inelastic helium atom scattering spectroscopy and time-of-flight techniques to measure the (001) surface phonon dispersion in both the topological and trivial phases. Surface lattice dynamics calculations are performed to interpret and characterize measured dispersion curves. Comparing the results of the two phases reveals a remarkable change in an optical phonon branch. A nearly-flat 9.0 meV shear-vertical surface resonance branch in the trivial phase is replaced in the topological phase with a new shear-vertical resonance that exhibits dramatic momentum-dependent softening down to a minimum of 5.8 meV at a momentum that coincides with 2kF of the emergent Dirac fermions. This softening clearly indicates strong screening of these surface phonon modes by the Dirac fermions and suggests further investigation of the underlying electron-phonon coupling. A quantitative calculation of the coupling between the electronic states and surface phonons is performed with the aid of a microscopic model based on linear Coulomb coupling of ionic displacements to the Dirac fermion density, which is incorporated in the phonon Matsubara Green’s function. The real part of the self-energy is fit to the experimental dispersion data and the imaginary part is obtained through a Kramers-Kronig transformation. Finally, this is used to calculate the corresponding momentum-dependent mode-specific electron-phonon coupling parameter λν(q). The coupling magnitude is found to reach values as high as 0.47, which is stronger than that in typical metals, but weaker than the values reported for the surfaces of the topological insulators Bi2Te3 and Bi2Se3.
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