Abstract
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 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 to ground states in AlAs confined systems is reevaluated.
- Received 14 May 2002
DOI:https://doi.org/10.1103/PhysRevB.66.235316
©2002 American Physical Society