Sum Rules for Reduced Matrix Elements of the Generalized Momentum Operator in III–V Semiconductors

Abstract

The band structure of III–V semiconductors near the Γ point is studied with full account of the spin-orbit interaction, which results not only in band splitting but also in spin-orbit mixing of wave functions of different spatial symmetry. In view of the last circumstance, a new version of the k·p method of perturbation theory is developed and strict symmetry relations are derived for the first time in which sums containing optical matrix elements and energy denominators are related to intrinsic electron characteristics (masses, g factors). These relations (sum rules) appear to be informative in analyzing the spatial symmetry of electronic states near the Γ point and are useful for quantitative estimation of the most important optical matrix elements.