Electronic Polarons in Non‐Metals with Short‐Range and Local‐Field Effects

The electronic polaron approximation (EPA) by Toyozawa does not deal correctly with the short range part of the interaction between a quasi‐particle and the polarization field of a non‐metal, owing to the use of a continuum approximation for the polarization field. A modified EPA is derived, without this continuum approximation, from a weak coupling zero order tight‐binding model. It includes short range and local field effects and leads to an electron self‐energy ∑ without the explicit first Brillouin zone cut‐off found when Toyozawa's EPA is used. A simple practical approximation is derived in order to take into account the non‐dipolar contributions which cannot be neglected when large wave vectors are involved. A physical cut‐off, scaled by the atomic or ionic radius is thus incorporated in the theory. The numerical significance of the continuum approximation for the polarization field is tested by comparison, with the elaborate calculations of Kunz. It is found that the short wave length contributions to ∑ may in no way be neglected if one want to improve significantly over the much simpler classical approximation (due to Mott and Littleton), as used by Fowler.