Abstract
The influence of the spin-orbit split-off band on the tunneling of holes across heterostructures is studied starting with the Luttinger-Kohn Hamiltonian. The latter is diagonalized into blocks (upper and lower Hamiltonians) using a unitary transformation. We consider and material systems, and study the tunneling of holes through a one-dimensional δ scatterer and across abrupt potential steps. In each case, we show that the presence of the spin-orbit split-off band has a profound influence on the transmission coefficients of holes, even for holes with energy much lower than the threshold for free propagation in the spin-orbit split-off band. For the potential steps, we show that the results can be quite different with upper and lower Hamiltonians. Furthermore, we stress the importance of the spin-orbit split-off band by comparing the results with those obtained with the Luttinger-Kohn Hamiltonian which neglects the importance of the spin-orbit split-off band.
- Received 3 November 1997
DOI:https://doi.org/10.1103/PhysRevB.58.16315
©1998 American Physical Society