Solutions of the k·p Hamiltonian in confined systems with a highly nonparabolic dispersion and consequences for AlAs quantum wells

We present two methods to deal with quantum confinement in systems with a camel's back dispersion. The two-band Hamiltonian for AlAs X states is solved both by analytical and transfer-matrix methods. The latter offers a general yet relatively simple and flexible way to deal with all types of potential profile. We calculate energy spectra and wave functions for single GaAs/AlAs/GaAs quantum wells and discuss the implications of our results on Γ-X_z mixing. We also determine the Landau level fan for AlAs systems with the magnetic field perpendicular to the camel's back axis. In both cases, we find the confined energies and wave functions to be greatly affected by the k·p interaction. We also show that the well-known type I-type II transition for GaAs/AlAs superlattices is modeled correctly by taking the k·p interaction into account, and that previous effective mass treatments are not reliable. In addition, the crossover from X_Z to X_Y, ground states in AlAs confined systems is reevaluated.