Variational Polaron Equations Applied to the Generalized Fröhlich Model*

Ab initio modeling of polarons is a vivid research area with various emerging approaches that allow the calculation of effective mass, localization length, and formation energy of these quasiparticles in various kinds of materials. Starting from recent advances in this field^1-4, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space⁵. In this framework, polaron formation energy as well as individual electron, phonon, and electron-phonon contributions are obtained. An efficient gradient-based optimization algorithm is suggested, and the generalized Fröhlich model^6-7 is investigated. This model extends the standard Fröhlich formulation to take into account optical phonon coupling to degenerate and anisotropic electronic bands, describing cubic polar materials. Within the proposed variational framework, the known asymptotic solution in isotropic non-degenerate limit is recovered. Further introduction of uniaxial anisotropy and band degeneracies leads to the symmetry breaking of polaronic solutions, which is systematically investigated in this work. 

Additionally, the variational approach is applied to investigate the formation of a Fröhlich polaron with an unusual shape in a real material, namely SnSe^8-9. We show that its exotic characteristics are due to the fine features of the valence band extrema, which are captured by the variational methodology.