Electron-phonon correlations on spin texture of gapped helical Dirac Fermions

The metallic surface states of a topological insulator support helical Dirac fermions protected by topology with their spin locked perpendicular to their momentum. They can acquire mass through magnetic doping or through hybridization of states on opposite faces of a thin sample. In this case there can be a component of electron spin oriented perpendicular to the surface plane. The electron-phonon interaction renormalizes the dynamics of the charge carriers through their spectral density. It also modifies the gap channel and a second spectral function enters which, not only determines the out of plane spin component, but also comes into in-plane properties. While the out of plane spin component is decreased below the Fermi momentum ($k_F$), the in plane component increases. There are also correlation tails extending well beyond $k_F$. The angular resolved photo-emission line shapes aquire Holstein side bands. The effective gap in the density of states is reduced and the optical conductivity aquires distinct measurable phonon structure even for modest value of the electron-phonon coupling.