Remarks on the Study of Electronic Properties and Photoionization Process in Rotating 2D Quantum Rings

TL;DR

This work analyzes electronic and optical properties of rotating 2D GaAs quantum rings using the Tan-Inkson confinement model in the presence of AB flux and a uniform magnetic field. It derives exact solutions for energies and wavefunctions, formulates the photoionization cross section via Fermi's golden rule with dipole coupling, and identifies a selection rule with $\Delta m=\pm1$. The study shows AB flux induces red/blue shifts and modulates PCS peaks, while decreasing ring radius increases peak strength and energy. Extending the model to a rotating frame, it demonstrates that rotation shifts probability densities, lifts degeneracy, and modifies energy spectra through $\varpi$, $\omega^{*}$, and related parameters, highlighting rich, tunable physics in 2D QRs with potential implications for optoelectronics, spintronics, and quantum information applications.

Abstract

Electronic and optical properties of a mesoscopic heterostructure of a two-dimensional quantum ring composed of Gallium Arsenide (GaAs) semiconductors are investigated. Using the confinement potential proposed by Tan-Inkson to describe the system under analysis, we conducted a numerical study of the photoionization cross section for a 2D quantum ring with and without rotation effects. The interior of the quantum ring is traversed by an AB flux. Our research aims to investigate how this mesoscopic structure's electronic and optical properties respond to variations in the following parameters: average radius, AB flux, angular velocity, and incident photon energy. Under these conditions, we establish that optical transitions occur from the ground state to the next excited state in the conduction sub-band, following a specific selection rule. One of the fundamental objectives of this study is to analyze how these rules can influence the general properties of two-dimensional quantum rings. To clarify the influence of rotation on the photoionization process within the system, we offer findings that illuminate the effects of the pertinent physical parameters within the described model. We emphasize that, although this is a review, it provides critical commentary, analysis, and new perspectives on existing research. Some results presented in this paper can be compared with those in the literature; however, new physical parameters and quantum ring configurations are used.

Figures (21)

• Figure 1: Schematic representation of the formation of energy bands in materials.
• Figure 2: Representation of two quantum rings with different average radius configurations: (a) $r_0 = 10\,\mathrm{nm}$ and $\hbar\omega = 25.6\,\mathrm{meV}$, suitable for studying optical properties; (b) $r_0 = 1000\,\mathrm{nm}$ and $\hbar\omega = 0.50\,\mathrm{meV}$, used to only study the electronic properties.
• Figure 3: Profile of the Tan-Inkson potential (Equation (\ref{['eq:v(r)inkson']})) and the harmonic approximation potential (Equation (\ref{['eq:parabola']})). The parameter used for (b) is $\hbar\omega_{0}=25.6~\mathrm{meV}$ and $r_{0}=10~\mathrm{nm}$. In (a), we have $r_{0}=10~\mathrm{nm}$ with the confinement energy $\hbar\omega_{0}$ varying from $0$ to $120~\mathrm{meV}$, with a range of $3.2~\mathrm{meV}$. The green curve $\hbar\omega_{0}=0~\mathrm{meV}$ does not generate a confinement potential; the red curve in (b) is the one plotted in (a).
• Figure 4: Three-dimensional graph of the Tan-Inkson potential (Equation (\ref{['eq:v(r)inkson']})). The parameter values used were $\hbar \omega_0=25.6~\mathrm{meV}$, $r_0=10~\mathrm{nm}$.
• Figure 5: Probability distribution plot for the first three quantum numbers $n$. The parameter values used are $\hbar \omega_0=25.6\,\mathrm{meV}$, $r_0=10\,\mathrm{nm}$, $\phi=0.1\,(h/e)$ and $B=0,2,4,6,\dots,20~\mathrm{T}$. The black curve in all the graphs represents the value of $B=20$.