Measuring, interpreting, and translating electron quasiparticle – phonon interactions on the surfaces of the topological insulators
Boston University, USA
I will present a comprehensive study of the interaction of Dirac fermion quasiparticles (DFQs) and phonons on the surfaces of the strong topological insulators Bi2Se3 and Bi2Te3. Inelastic helium atom surface scattering (HASS) spectroscopy was used to measure the surface phonon dispersion of these materials along the two high-symmetry directions of the surface Brillouin zone (SBZ). Two anomalies shared by both of these materials are manifest in the experimental data. First, the absence of surface Rayleigh acoustic waves, which points to significantly weak coupling between the DFQs and the surface acoustic phonon modes. Second, both materials exhibit low-lying surface optical phonon branch with vertical shear polarization; which starts at the SBZ center and disperses to lower energy with increasing wave vector along both high-symmetry directions of the SBZ. This downward 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 arising from strong interaction of this surface phonon mode with the DFQs.
To quantify the coupling between the low-lying optical phonon branch that couples strongly to the DFQs a phenomenological model was constructed based on 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 DFQ-phonon coupling λν(q) from experimental data. Moreover, an averaged coupling parameter was determined for both materials yielding λTe ≅ 2 and λSe ≅ 0.7. These values are significantly higher than those of typical metals.
In an effort to connect electron-phonon coupling obtained from experimentally measured surface phonon dispersions with their counterparts obtained from photoemission spectroscopies, we developed a method based on the Matsubara Green's function formalism. A DFQ Matsubara function was constructed. It contained DFQ-phonon interactions manifest in the matrix elements obtained from the RPA model fitting to the optical phonon branch, as well as the phonon Matsubara function. A computational process was then developed that allowed the scenario of translating the electron-phonon interaction from the phonon perspective to the DFQ perspective. This scenario involved the calculation of the real and imaginary parts of the DFQ self energy and, subsequently, DFQ spectral function and the density of states. A direct comparison with photoemission and scanning tunneling spectroscopies results was then possible. The features present in the spectral function were quite valuable in setting the requisite energy resolution for reliable determination of the electron-phonon coupling, and in evaluating different methodologies for determining λ from experimental data pertaining to the DFQs. It is also worth noting that extracting λ from the calculated spectral functions yields results identical to those obtained from HASS, proving the self-consistency of the approach.