No abstract

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-Lüttinger 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.

Meaningful and well-founded physical quantities are convincingly determined by eigenvalue problem solutions emerging from a second-order N -coupled system of differential equations, known as the Sturm-Liouville matrix boundary problem. Via the generalized Schur decomposition procedure and imposing to the multicomponent system to be decoupled, which is a widely accepted remarkable physical situation, we have unambiguously demonstrated a simultaneously triangularizable scenario for (2N × 2N ) matrices content in a generalized eigenvalue equation.