Low-energy theory for electron-phonon scattering in topological insulators

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This project is aimed at advancing the low-energy theory of electron-phonon scattering effects for the surface Dirac fermions in three-dimensional strong topological insulators, in particular in Bi2Se3 and Bi2Te3. We will consider different geometries, including cylindrical and/or rectangular nanowires, thin films, and semi-infinite samples.Three subprojects summarize and structure our main objectives:1) We will study electron-phonon coupling effects on the surface Dirac fermions in topological insulator nanowires. In particular, we will quantitatively determine the effective electron-phonon coupling strength, the phonon-induced magneto-resistivity contribution, the quasiparticle lifetime, and the phase coherence length. We shall consider nanowires with circular and/or rectangular cross-section, study the case of arbitrary temperatures, and fully take into account magnetic field effects and variations of the Fermi level.2) We will analyze intrinsic limits on spin-dependent ballistic surface state transport in strong topogical insulators due to the coupling to acoustic phonons. We plan to study the semi-infinite and the thin-film geometry by computing the spin relaxation rate and the spin resistivity as a function of temperature, doping level, and magnetic field.3) Electron-phonon scattering in topological insulators so far has only been discussed the case of finite doping, i.e., away from the Dirac point. When the Fermi energy is close to the Dirac point, non-perturbative approaches are needed. We will approach this many-body problem within a functional integral approach for the semi-infinite geometry. Using the resulting effective low-energy theory for the surface Dirac fermions, we will study the temperature dependence of the resistivity and of the quasiparticle lifetime. Magnetic field effects will be included in our analysis, and we shall explore whether charge- and/or spin-density wave phases could be realized. We also plan to investigate the prospects for surface superconductivity.