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.

We present the metamorphosis in the effective-potential profile of layered heterostructures, for several III-V semiconductor binary compounds, when the band mixing of light and heavy holes increases. A root-locus-like procedure, is directly applied to an eigenvalue quadratic problem obtained from a multichannel system of coupled modes, in the context of multiband effective mass approximation. By letting grow valence-band mixing, it is shown the standard fixed-height rectangular potential-energy for the scatterer distribution, to be a reliable test-run input for heavy holes. On the contrary, this scheme is no longer valid for light holes and a mutable effective \emph{band offset} profile has to be considered instead, whenever the in-plane kinetic energy changes.Comment: 12 pages, 5 figure

No abstract

A new approach based on a polynomial-scattering formalism was developed and exercised for n-cell multi-channel layered heterostructures. The model reproduces the majority of considered experimental measurements, better than prior theoretical results. Closed analytical formulae of scattering quantities for uncoupled particles of multiband-multicomponent systems have been derived; furthermore, long-standing numerical difficulties of the transfer matrix scheme were overcome. We predict the earlier arrival of uncoupled holes and several patterns followed by the transmission rate, the two-probe Landauer total conductance, and the phase time. Anomalous events such as the Ramsauer-Townsend oscillations and the paradoxical Hartman effect of pure holes are confirmed in detail; besides, we predict other appealing structural-dependent features to be tuned as well. For such quasi-particles, we do not find evidence of the generalized Hartman effect. The relevant phase tunneling time limit of bandmixing-free holes when n→∞ has been resolved analytically as well as simulated, and it turns qualitatively comparable with that measured for photons. At the request of the authors, this article is being retracted effective 17 November 2021.