Resonance states in a cylindrical quantum dot with an external magnetic field

TL;DR

This paper investigates the behavior of resonance states in a cylindrical quantum dot under an external magnetic field, revealing how Landau levels influence resonance binding and localization in different physical regimes.

Contribution

It introduces a detailed analysis of resonance states in a quantum dot with magnetic field effects using the complex rotation method, highlighting the influence of Landau levels.

Findings

Resonance states are strongly affected by Landau levels.

Two physical regimes identified based on field strength and quantum dot size.

Localization probability and fidelity reveal resonance binding mechanisms.

Abstract

Bound and resonance states of quantum dots play a significant role in photo-absorption processes. In this work, we analyze a cylindrical quantum dot, its spectrum and, in particular, the behaviour of the lowest resonance state when a magnetic field is applied along the symmetry axis of the cylinder. To obtain the energy and width of the resonance we use the complex rotation method. As it is expected the structure of the spectrum is strongly influenced by the Landau levels associated to the magnetic field. We show how this structure affects the behaviour of the resonance state and that the binding of the resonance has a clear interpretation in terms of the Landau levels and the probability of localization of the resonance state. The localization probability and the fidelity of the lowest energy state allows to identify two different physical regimes, a large field-small quantum dot radius regime and a small field-large quantum dot radius, where the binding of the resonance is dominated by the field strength or the potential well, respectively.