Effective particles in a multishell nanostructure with hardcore

TL;DR

This paper analytically studies in-medium effective carriers with position-dependent mass in a multishell heterostructure, deriving exact eigenstates and applying results to optical properties of GaAs/Al-GaAs nanostructures.

Contribution

It provides exact solutions for bound and scattering states in a multishell heterostructure with position-dependent mass, including analysis of optical properties and the impact of Hamiltonian ordering.

Findings

Exact spectrum of bound eigenstates obtained

Optical properties like absorption coefficients calculated

Dependence of results on Hamiltonian ordering class analyzed

Abstract

In-medium effective carriers with position-dependent mass in a multishell heterostructure are analytically studied. We obtain the exact spectrum of three-dimensional bound eigenstates and the scattering wave-functions for several von Roos ordering classes. Ascribing a continuously varying mass to the carriers in a multilayer type spherical system we use our solutions to compute optical properties such as the absorption coefficients and refraction indices of a nanometric heterostructure. We analyze in detail the case of a GaAs/Al-GaAs alloy and show how these results depend on the ordering class of the kinetic Hamiltonian.