Polaron effective mass and localization length in cubic materials: degenerate and anisotropic electronic bands

The polaron notion is almost one century old, yet most works on polaron models, to understand their characteristics such as radius, effective mass, mobility and energy dispersion, have focused on the original Fröhlich model for large polarons, with a simple (non-degenerate) parabolic isotropic electronic band coupled to one dispersionless longitudinal optical phonon mode [1]. Real cubic materials have electronic band extrema that are often degenerate (e.g. 3-fold degeneracy of the valence band), or anisotropic (e.g. conduction bands at X or L)[2]. We go beyond the existing isotropic [3] and non-degeneracy hypotheses, and provide, for polaron effective masses (at the lowest order of perturbation theory), and for localization lengths (variational approach), with multiple phonon modes: (i) the analytical result for the case of anisotropic electronic energy dispersion, with two distinctive effective masses (uniaxial), (ii) an expression for the case of three distinctive axes (ellipsoidal), (iii) numerical simulations for the 3-band degenerate case, applied to III-V and II-VI semiconductor valence bands.

[1] G. D. Mahan, Many-Particle Physics (Springer, NY, 2014)
[2] A. Miglio et al., npj Comput Mater 6, 167 (2020)
[3] H. R. Trebin and U. Rössler, Phys. Stat. Sol. (b), 70:717-726 (1975)