Generalized Fröhlich model vs accurate first-principles: zero-point renormalisation in polar semiconductors and insulators.

Computing the zero-point renormalization (ZPR) of the electronic bandgap due to electron-phonon coupling from first principles (FP) is a computationaly challenging task, especially for polar materials, for which a very fine phonon wavevector sampling is required [1]. By contrast, the well-known Fröhlich Hamiltonian gives in the perturbative regime a simple analytical formula for the polaron binding energy, based on a few parameters that can be obtained from experiments or from FP calculations.

We compute the ZPR from FP for more than 20 polar binary semiconductors and insulators, and compare these results to those from a generalized Fröhlich model, in which the needed parameters are computed from FP. Despite the lack of Debye-Waller (DW) and interband contributions, we find that the simple Fröhlich approach agrees with FP results within a factor of two for most materials. We analyze the cancellation between the DW and Fan contributions from acoustic modes, and discuss the size of interband contributions in terms of Eliashberg functions. We finally develop a method to estimate the converged ZPR from coarser phonon samplings.

[1] G. Antonius et al, PRB 92, 085137 (2015); S. Poncé et al, J. Chem. Phys. 143, 102813 (2015).