Generalized eigenvalue problem criteria for multiband-coupled systems: hole mixing phenomenon study

Non-linear eigenvalue equations straightforwardly determine fundamental physical quantities of a wide variety of areas. We retrieve a root-locus-like procedure, as a new technique for directly analyzing specific physical phenomena involving multiband-multichannel charge–carrier coupled modes. A new explicit necessary and sufficient condition is presented for a generalized eigenvalue problem, associated with an N-coupled components matrix boundary equation. Within our approach, the uncoupled-system case is nicely recovered. We tested the present scheme by applying it to heavy and light holes, described via the Kohn–Luttinger model, and found good agreement for our proposition even at medium-intensity band mixing. We simulated the multiband-hole band-mixing-phenomenon by monitoring the root-locus for the quadratic eigenvalue problem, and by plotting the metamorphosis of the effective band offset profile, for bulk and layered heterostructures, respectively. Several new features have been observed; for example, for light holes solely, an appealing interchange of quantum-well-like versus barrier-like roles has been detected for several III–V semiconductor binary compounds.