AA-stacked Bilayer Graphene Quantum Dots in Magnetic Field

TL;DR

This paper analytically studies the energy spectrum and wave functions of AA-stacked bilayer graphene quantum dots under a magnetic field, revealing unique symmetry properties and confinement regimes compared to other quantum dot systems.

Contribution

It provides an analytical solution for confined states in AA-stacked bilayer graphene quantum dots with magnetic field, highlighting symmetry breaking and confinement regimes.

Findings

Energy spectrum consists of two shifted copies of single-layer graphene spectrum.

Magnetic field breaks most symmetries except intervalley electron-hole symmetry.

Two confinement regimes identified: weak B with infinite-mass barrier, strong B dominated.

Abstract

By applying the infinite-mass boundary condition, we analytically calculate the confined states and the corresponding wave functions of AA-stacked bilayer graphene quantum {dots} in the presence of an uniform magnetic field $B$. It is found that the energy spectrum shows two set of levels, which are the double copies of the energy spectrum for single layer graphene, shifted up-down by $+\gamma$ and $-\gamma$, respectively. However, the obtained spectrum exhibits different symmetries between the electron and hole states as well as the intervalley symmetries. It is noticed that, the applied magnetic field breaks all symmetries, except one related to the intervalley electron-hole symmetry, i.e. $E^e(\tau,m)=-E^h(\tau,m)$. Two different regimes of confinement are found: the first one is due to the infinite-mass barrier at weak $B$ and the second is dominated by the magnetic field as long as $B$ is large. We numerically investigated the basics features of the energy spectrum to show the main similarities and differences with respect to monolayer graphene, AB-stacked bilayer graphene and semiconductor quantum dots.