Polarons in the Degenerate‐Band Case

Abstract

The Frohlich polaron model has been applied so far only to the case of electron states with simple parabolic bands. An extension is given of the polaron concept to more complex states as e.g. the valence bands in zincblende-type crystals. The band structure is described as in the spherical model of Baldereschi and Lipari. The electron-phonon interaction in the Frohlich approximation is treated by perturbation theory. Besides a renormalization of the band parameters the electron-phonon coupling results in a partial mixing of electronic states from different subbands, i.e. of light and heavy holes.

Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors: Results for zinc-blende GaN

“…In the isotropic case, it is shown in [44] how the renormalization is an average of the light and heavy holes at k=0. We can average the effective mass of each band over a sphere using Eq.…”

Fröhlich polaron effective mass and localization length in cubic materials: Degenerate and anisotropic electronic bands

“…In contrast, if A = B + C, one obtains the isotropic threefold degenerate case, in which, irrespective of the wave-vector direction, there is a nondegenerate band, with inverse effective mass m −1 0 = 2A and two degenerate bands with effective mass m −1 1 = 2B. This case has been tackled by Trebin and Rössler [32], who provide the analytical expression for the self-energy and effective masses in the one-phonon branch hypothesis. The present formalism delivers exactly the same analytical expressions for the effective masses in such case, but also generalizes them to the multiphonon case.…”

“…So far, there have only been a few attempts to formulate and study an extended model beyond the above-mentioned simplifying hypotheses. Trebin and Rössler [32] studied polaron energies and effective masses in the case of triply degenerate bands, however without the inclusion of band warping (they worked with "isotropic" triply degenerate bands), and ignored the effect of multiple LO phonon branches. Similarly, Fock, Kramer, and Büttner [33] examined polaron energies and masses in the nondegenerate case with uniaxial symmetry for effective mass (and dielectric tensor), but considered only one LO phonon branch.…”

“…To our knowledge, the strong-coupling limit has not been examined in any of these cases. Trebin and Rössler [32] also considered the effect of spin-orbit coupling. It is not considered in the present paper, and must be the subject of future work.…”

Polarons and Wannier Excitons in Anisotropic Polar Crystals

“…The effect of electron-phonon coupling on the electron-hole interaction in a Wannier exciton has been thoroughly studied already by Haken in the case of simple parabolic bands [3]. Exciton and polaron problems in polar crystals have been investigated more recently in order to consider some aspects of real semiconductors : the degeneracy of the valence band, which is typical for most cubic semiconductors [4]; the mass anisotropy of carriers in otherwise isotropic semiconductors with multi-valley band structure [5] ; and the combined effect of mass anisotropy and anisotropic electron-phonon interaction in anisotropic polar crystals [6, 71. I n this paper we reconsider the polaron and exciton problems in an anisotropic polar semiconductor in order to improve some of the previous results. For the anisotropic polaron the electron-phonon coupling has been considered so far only in secondorder perturbation theory [6] which is applicable only for small coupling constants.…”