Theory of Confined States of Positronium in Spherical and Circular Quantum Dots with Kane's Dispersion Law

TL;DR

This paper theoretically investigates the confined states of positronium in spherical and circular quantum dots, analyzing how quantum confinement and dispersion laws affect binding energies and formation dependence on dot size.

Contribution

It introduces a theoretical model for positronium states in quantum dots considering Kane's dispersion law and compares it with parabolic models, highlighting the role of dimensionality.

Findings

Positronium instability arises from dimensionality reduction.

Binding energies depend on quantum dot size and shape.

Positronium formation varies with quantum dot radius.

Abstract

Confined states of a positronium (Ps) in the spherical and circular quantum dots (QDs) are theoretically investigated in two size-quantization regimes: strong and weak. Two-band approximation of Kane dispersion law and parabolic dispersion law of charge carriers are considered. It is shown that the electronpositron pair instability is a consequence of dimensionality reduction, not of the size quantization (SQ). The binding energies for the Ps in circular and spherical QDs are calculated. The Ps formation dependence on the QD radius is studied.