Aharonov-Bohm flux and dual gaps effects on energy levels in graphene magnetic quantum dots

TL;DR

This paper investigates how Aharonov-Bohm flux influences energy levels in graphene magnetic quantum dots with internal and external gaps, revealing tunable electronic properties and potential for quantum device control.

Contribution

It provides an analytical model showing the effects of AB flux and dual gaps on energy levels and band gaps in graphene quantum dots, highlighting tunability of electronic properties.

Findings

AB flux increases band gap width when internal gap is present

Energy levels exhibit symmetric or asymmetric behavior depending on valleys and angular momentum

Higher AB flux reduces levels between conduction and valence bands, enlarging the band gap

Abstract

We address the question of how the Aharonov-Bohm flux $\Phi_{AB}$ can affect the energy levels of graphene magnetic quantum dots (GMQDs) of radius $R$. To answer this question, we consider GMQDs induced by a magnetic field $B$ and subjected to two different gaps - an internal gap $\Delta_1$ and an external gap $\Delta_2$. After determining the eigenspinors and ensuring continuity at the boundary of the GMQDs, we formulate an analytical equation describing the corresponding energy levels. Our results show that the energy levels can exhibit either a symmetric or an asymmetric behavior depending on the valleys $K$ and $K'$ together with the quantum angular momentum $m$. In addition, we find that $\Phi_{AB}$ causes an increase in the band gap width when $\Delta_1$ is present inside the GMQDs. This effect is less significant when a gap is present outside, resulting in a longer lifetime of the confined electronic states. Further increases in \(\Phi_{AB}\) reduce the number of levels between the conduction and valence bands, thereby increasing the band gap. These results demonstrate that the electronic properties of graphene can be tuned by the presence of the AB flux, offering the potential to control the behavior of graphene-based quantum devices.