Study of the transition from resonance to bound states in quantum dots embedded on a nanowire using the $\mathbf{k}\cdot\mathbf{p}$ method

TL;DR

This paper investigates how quantum dot states in semiconductor nanowires transition from resonant to bound states under magnetic fields, using the k method, revealing scenarios for state transformation.

Contribution

It introduces a detailed analysis of state transitions in quantum dots within nanowires using the k method, highlighting the conditions for transforming resonances into bound states.

Findings

Discrete energy levels depend on magnetic field strength.

States can transition from resonances to bound states and vice versa.

Multiple scenarios for state transformation are identified.

Abstract

We study the band structure of semiconductor nanowires with quantum dots embedded in them. The band structure is calculated using the Rayleigh-Ritz variational method. We consider quantum dots of two different types, one type is defined by electrostatic potentials applied to the nanowire, while the other one is defined by adding materials with band offsets with respect to the band parameters of the nanowire. We are particularly interested in the appearance of discrete energy levels in the gap between the conduction band and the valence band of the nanostructure, and in the dependence of the energy of these levels with the intensity of a magnetic field applied along the wire. It is shown that several scenarios are possible, being of particular interest the possibility of transforming states of the discrete into resonances and vice versa.