2.11. Interface Hamiltonian 8-band Zinc-Blende

2.11.1. The Model

The interface Hamiltonian is used to model the heterostructures with atomic sharp interfaces. This is an extension of the standard 8-band \(\mathbf{k} \cdot \mathbf{p}\) model (described here). The model, originally derived in [Kilpstein2010], includes \(l=2\) perturbation terms, which have been omitted in our implementaion, consistent with the approach in [LivnehPRB2012].

The interface Hamiltonian in the block form is given by:

\[\begin{split}\hat{\mathcal{H}}_{interface} = \delta (z - z_{i}) \begin{bmatrix} D_S & 0 & 0 & \pi \beta \\ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0 & D_X & \pi \alpha & 0 \\ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0 & \pi \alpha & D_X & 0 \\ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pi \beta & 0 & 0 & D_Z \\ \end{bmatrix}\end{split}\]

where \(\delta\) is the Dirac delta function, \(z_{i}\) is the position of the interface, \(D_S\), \(D_X\), \(D_Z\), \(\alpha\), and \(\beta\) are the interface Hamiltonian parameters, \(\pi\) is the parameter that can take values of \(\pm 1\). Parameter \(\pi\) is used to distinguish different ordering of materials at the interface, for example InaAs/GaSb and GaSb/InAs interfaces would have same interface paramters, but opposite \(\pi\) values.

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Last update: 07/01/2026