Electron-Phonon Interaction: Band-Gap Renormalization, High-Throughput Analysis of Polaron Models, Contribution to Total Energy

Electronic properties are affected by atomic motion through electron-phonon interaction, even at 0 K, due to zero-point motion. This effect, named “zero-point renormalization” (ZPR) is ignored in most first-principles calculations, although sometimes included within the adiabatic approximation. I report first the first-principles evaluation of zero-point renormalization beyond the adiabatic approximation for 30 materials [1,2]. When light elements (e.g. oxygen) are present, ZPR is often larger than 0.3 eV and can be bigger than 1 eV. This effect cannot be ignored if accurate band gaps are sought: it is useless to go beyond G0W0 without including ZPR effects in such materials. For infrared-active materials, global agreement with available experimental data is obtained only when nonadiabatic effects are taken into account. They are well represented by a generalized Fröhlich model (multiple phonon bands, degenerate electronic states, anisotropic).
The standard Fröhlich (one phonon band, non-degenerate electronic state, isotropic) model is actually a workhorse for the large polaron community, used for decades. In the second part of this presentation [3], the domain of validity of the standard Fröhlich model and its generalized version is tested against first-principles data for a large set of 1260 materials. Also, its perturbative treatment is tested. Among this extended dataset, most materials host perturbative large polarons, but there are many instances that are non-perturbative and/or localize on distances of a few bond lengths. A variety of behaviours is found, with the statistical characterization of these for this large set of materials.
Finally, I will discuss the contribution of the electron-phonon interaction to the total energy. Based on a proposal from Ph. Allen, A. Varma and collaborators [4] compute such a contribution and claim it is the key to explaining the energy ordering in SiC polymorphs. I will show that the formula from Ph. Allen is not an electron-phonon contribution to the total energy, but a double counting of a part of the zero-point phonon energy.