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

## TL;DR

This paper introduces a numerical method to analyze complex bandmixing phenomena in layered semiconductor systems using a quadratic eigenvalue problem approach, revealing new spectral features influenced by spin-split hole interactions.

## Contribution

The study develops a novel computational procedure based on QEP to accurately model multiband coupling in semiconductor heterostructures, extending previous models to include spin-split hole effects.

## Key findings

- Successfully models heavy, light, and spin-split holes in heterostructures.
- Reveals significant influence of spin-split hole interactions on spectral properties.
- Refines conditions for generalized quadratic eigenvalue problems.

## Abstract

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