Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to ZPR can be understood in terms Fr\"ohlich model, which focuses on nonadiabatic interaction between an electron macroscopic electrical polarization created a long-wavelength optical longitudinal phonon mode. On other hand, spin-orbit (SOC) modifies bare structure, will, turn, affect ZPR. We present comparative investigation effect SOC twenty with cubic symmetry using first-principles calculations. observe SOC-induced decrease ZPR, up 30%, driven valence edge, almost entirely originates from modification eigenenergies hole effective masses near $\mathrm{\ensuremath{\Gamma}}$ point. also incorporate into generalized addressing Dresselhaus splitting occurs noncentrosymmetric confirm that predominance effects materials unchanged when including SOC. Our model provides reliable estimate polaron formation energy obtained first principles brings light some fundamental subtleties numerical evaluation for materials. finally warn about possible breakdown parabolic approximation, one assumptions within physically relevant range high frequencies treated