Electron state symmetries and optical transitions in semiconductor superlattices .1. (GaAs)(m)(AlAs)(n) grown along the [001] direction

Using the method of induced band representations of space groups, we have performed a complete group-theory analysis of electron state symmetries in (GaAs)(m)(AlAs)(n) superlattices grown along the [001] direction. The spin-orbit interaction has been taken into account. The selection rules for both direct and phonon-assisted optical transitions have been derived. Using both the results of our group-theory analysis and data on the various electronic-structure calculations which have appeared in the literature, we predict some variations in the optical transitions when m and/or n are varied. We also propose optical experiments to decide among the numerous and sometimes contradictory results of those band calculations.