HOLE SUBBAND STATES OF GAAS/ALXGA1-XAS QUANTUM-WELLS WITHIN THE 6X6 LUTTINGER MODEL

We present an exact solution for the hole subband dispersion of a [001] symmetric GaAs/Al-x Ga1-xAs quantum well within the 6X6 Luttinger model, which extends previous work by Andreani, Pasquarello, and Bassani, Phys. Rev. B 36, 5887 (1987) for the 4X4 case. We employ symmetry arguments to decouple the Kramers doubly degenerate subband states and build well-defined parity states of the quantum-well reflection operator, which include the spin-split-off band. Numerical results are presented for the hole subband states and in-plane dispersion curves of a 66-Angstrom AlAs-GaAs-AlAs quantum well, which show anticrossing behavior. The nature of anticrossings between the first and second and the eighth and ninth subbands is investigated by studying the bulk state decomposition of the envelope functions. In the vicinity of the first and second subband anticrossing, there is a negligible bulk GaAs spin-split-off band content. In contrast, in the region of the anticrossing for the higher eighth and ninth subband states, there is considerable GaAs spin-split-off band amplitude, as the GaAs spin-split-off band is nearby in energy.