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

Laura E. Bremme and P. C. Klipstein
Phys. Rev. B 66, 235316 – Published 20 December 2002
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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 ΓXZ 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 kp interaction. We also show that the well-known type I–type II transition for GaAs/AlAs superlattices is modeled correctly by taking the kp interaction into account, and that previous effective mass treatments are not reliable. In addition, the crossover from XZ to XX,Y 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

Authors & Affiliations

Laura E. Bremme and P. C. Klipstein

  • Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom

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Issue

Vol. 66, Iss. 23 — 15 December 2002

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