The Four-Band Spin-Less Kane Model in Curvilinear Coordinates

The possibility to fabricate complicated nanostructure geometries with novel topological effects so as to tailor physical properties makes it adamant to develop advanced analytical and numerical methods. The first multiband k · p model in general curvilinear coordinates based on Kane's four‐band spin‐less model for the upper conduction and valence band states is developed.

The model captures the combined effects of electron and light‐hole bandstructure coupling and curvature effects. The formulation in curvilinear coordinates allows to obtain a simple set of equations, displaying directly the influence of the local curvature, and the explicit equation sets in the cases of a torus and a helix‐shaped nanowire structure with a square cross section are given.

The presented derivation can be generalized to other types of k · p multiband models.