Electron-phonon interaction on the surface of a 3D topological insulator

TL;DR

This paper investigates how surface phonons interact with Dirac electrons on a 3D topological insulator, showing limited phonon renormalization and no induced surface superconductivity under ideal conditions.

Contribution

It provides a detailed analysis of electron-phonon coupling effects on the surface of topological insulators, highlighting the limited impact on phonon dispersion and superconductivity.

Findings

Rayleigh phonons are not strongly renormalized in ideal conditions.

Electron-phonon interaction is too weak to cause surface superconductivity.

Backscattering suppression reduces electron-phonon coupling effects.

Abstract

We analyze the role of a Rayleigh surface phonon mode in the electron-phonon interaction at the surface of a 3D topological insulator. A strong renormalization of the phonon dispersion, leading eventually to the disappearance of Rayleigh phonons, is ruled out in the ideal case of a continuum long-wavelength limit, which is only justified if the surface is clean and defect free. The absence of backscattering for Dirac electrons at the Fermi surface is partly responsible for the reduced influence of the electron-phonon interaction. A pole in the dielectric response function due to the Rayleigh phonon dispersion could drive the electron-electron interaction attractive at low frequencies. However, the average pairing interaction within the weak coupling approach is found to be too small to induce a surface superconducting instability.