Exact symmetries of electron states and optical selection rules in wurtzite-based nanostructures - art. no. 205312

The crystal structure of wurtzite-based (hexagonal) quantum wells (QW's), s uch as (GaN)(m)/AlN ones for example, is found to be described by the layer group P3m1 (DG69) and does not depend on the number of atomic monolayers c onstituting the QW whereas the symmetry of wurtzite-based superlattices (SL 's), such as (GaN)(m)(AlN)(n) ones for example, has been previously shown t o be described by the space groups C-3 upsilon(1) or C-6 upsilon(4) dependi ng on m + n is even or odd. The P3m1 (DG69) group is a factor group of the C-3 upsilon(1) group, the latter being the product of the P3m1 group and th e subgroup containing the translations along the z axis. Basing on these sy mmetries, we have determined the exact symmetries of Bloch states at the Ga mma and other symmetry points of the Brillouin zones of QW's and SL's and d erived optical selection rules for carriers and excitons. The latters prese nt large Rydberg values. We have shown that the built-in electric field, di rected along the z axis due to the symmetry, breaks the translational invar iance of the SL's along this direction reducing their symmetry to that of a single QW. We have established that when one (several) phonon(s) is (are) involved in a radiative process, it is always possible to connect any initi al state to any final one. The energy of the emitted photon depends on the nature of the phonon(s) if several channels are allowed for the transition. The symmetry of electron states in very thin QW's and short-period SL's is shown to be determined by their exact symmetry rather than that implied in envelope function approximation (EFA). Within the domain of validity of th e EFA, i.e., for not too thin layers, a detailed analysis of the Bloch-stat e symmetry is performed on imposing the invariance of the structure under t he change of z to -z (the sigma (z) symmetry operation). The correspondence is established between the symmetry of a Bloch state and the parity with r espect to sigma (z) of its associated envelope function. It is shown that E FA artificially induces a splitting of energy levels and appearance of new dark excitons.