Symmetry based calculation of electronic structure and intraband absorption in GaN/AlN hexagonal quantum dot superlattices

A symmetry based method for the efficient calculation of single-particle states in hexagonally symmetric GaN/AlN quantum dots within the framework of a k · p model is presented. The envelope functions are expanded into a plane wave basis on a hexagonal lattice and the group projector method is used to adapt the basis to exploit the symmetry, resulting in block diagonalization of the corresponding Hamiltonian matrix into six matrices and classification of the states by the quantum number of total quasi-angular momentum. The method is applied to the calculation of the electron and hole energy levels in a quantum dot superlattice and the intraband optical absorption matrix elements.