Influence of spin-orbit coupling and Rashba interaction on the electron-phonon renormalized electronic energy levels*

Electron-phonon (e-p) interaction calculations from first-principles are well documented in the literature. The predominance of non-adiabatic effects in the zero-point renormalization (ZPR) of the band gap for polar materials has been recently assessed in the light of the Fröhlich interaction.

Yet, even for benchmark materials, spin-orbit coupling (SOC) is frequently neglected to reduce the numerical cost of calculations. SOC manifests itself in the electronic structure through the split-off energy and by lifting band degeneracies away from time-reversal invariant momenta (TRIM). This modification of the energy levels will affect both e-p coupling energies and ZPR. Materials lacking inversion symmetry also exhibit an in-plane shift of the band extrema away from the TRIM, known as Rashba splitting. This could lead to resonant couplings at finite phonon wavevectors, which will strengthen the EP coupling energies.

We explicitly compute e-p coupling energies and ZPR for binary semiconductors, using density-functional perturbation theory (DFPT), with and without SOC. We also investigate Rashba semiconductor BiTeI. We finally analyze our results in the light of a three-dimensional Fröhlich Hamiltonian, including both SOC and Rashba interaction.