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We present a numeric-computational procedure to deal with the intricatebandmixing phenomenology in the framework of the quadratic eigenvalue problem(QEP), which is derived from a physical system described by N-coupledcomponents Sturm-Liouville matrix boundary-equation. The modeling retrieves thegeneralized Schur decomposition and the root-locus-like techniques to describethe dynamics of heavy holes (hh), light holes (lh) and spin-split holes (sh) inlayered semiconductor heterostructures. By exercising the extended (N = 6) KohnL\"uttinger model, our approach successfully overcomes the medium-intensityregime for quasi-particle coupling of previous theoretical studies. As a bonus,the sufficient conditions for a generalized QEP have been refined. Thesh-related off -diagonal elements in the QEP mass-matrix, becomes a competitorof the bandmixing parameter, leading the hh-sh and lh-sh spectral distributionto change, then they can not be disregarded or zeroed, as was assumed inprevious theoretical studies. Thereby, we unambiguously predict that several ofthe new features detected for hh-lh-sh spectral properties and propagatingmodes, become directly influenced by the metamorphosis of the effectiveband-offset scattering profile due sub-bandmixing effects strongly modulatedwith the assistance of sh, even at low-intensity mixing regime.

A bandmixing treatment for multiband-coupled systems via nonlinear-eigenvalue scenario