Exact symmetries of electron Bloch states and optical selection rules in [001] GaAs/AlAs quantum wells and superlattices - art. no. 205326

We determined the exact symmetries of conduction and valence Bloch states i n type-I and type-II [001] (GaAs)(m)(AlAs)(n) superlattices at the Gamma po int and at some other symmetry points of the Brillouin zone of the superlat tices and derived optical selection rules. Contrary to a result widely acce pted in the envelope-function approximation (EFA), p(z) atomic orbitals can not mix with p(x) and p(y) orbitals to build Bloch states. The phonon-assis ted transitions involving the Gamma point as an initial or final state are allowed both without and with taking into account the spin-orbit interactio n whatever are the symmetries of the initial and final states. The electron band structure of the superlattices is discussed. Within the domain of val idity of EFA (i.e., for not too small values of in and n), a detailed analy sis of the Bloch-state symmetry and selection rules is provided on imposing invariance of the superlattice structure under the change of z to -z (the sigma (z) symmetry operation). It is shown that optical transitions between the conduction states arising from the Gamma states of GaAs on one hand an d the conduction states arising from the X states of AlAs on the other hand can be allowed from spin-orbit coupling only. The correspondence is provid ed between the symmetry of a Bloch state and the parity with respect to sig ma (z) of its associated envelope function. The effect of an electric field parallel to the growth axis is discussed. Quantum wells do not differ from superlattices with regard to Bloch-state and envelope-function symmetries or optical selection rules. All the above results are still valid for any p seudomorphic superlattice or quantum well made of two binary compounds with zinc-blend structure and identical cations or anions, such as, for example , in the GaN/AlN system.