The Luttinger-Kohn theory for multiband Hamiltonians: A revision of ellipticity requirements

Understand

Modern applications require a robust and theoretically solid tool for the realistic modeling of electronic states in low dimensional nanostructures.

• The $k \cdot p$ theory has fruitfully served this role for the long time since its establishment.
• During the last three decades several problems have been detected in connection with the application of the $k \cdot p$ approach to such nanostructures.
• These problems are closely related to the violation of the ellipticity conditions for the underlying model, the fact that has been largely overlooked in the literature.