AA-stacked bilayer graphene quantum dots in magnetic field

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 +γ and −γ, 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 (τ, m) = −E h (τ, 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.

Energy levels of an ideal quantum ring in AA-stacked bilayer graphene

“…The green and red curves correspond, respectively, to −10 ≤ m ≤ −1 and 1 ≤ m ≤ 10, while the blue one corresponds to m = 0. For U = 0meV ( Figure 2(a) and (c)), we see that the energy spectrum shows two set of levels and the energy spectrum for U = 0meV resembles those found in the case of AA-stacked bilayer graphene quantum dot [28]. It is clear that the two set of this AA-stacked bilayer are just double copies of the energy spectrum corresponding to monolayer graphene one, shifted up/down by = +/ − γ.…”

Energy levels of monolayer -- AA-stacked bilayer graphene quantum dots

“…The A1 and B2 sites are coupled via a nearest-neighbor interlayer hopping term γ = 0.2 eV. The Bilayer graphene Hamiltonian in the vicinity of the K point is given by [27,28]…”

Circular quantum dots in twisted bilayer graphene

“…At θ = 0 and θ = 60 • , the tBLG structure turns into a prefect AA-and AB-stacked BLG QD, respectively (see the corresponding energy spectra in Refs. 39,42 ).…”

“…The studies show that the electronic and optical properties of graphene QDs can be tuned by size, shape, edge type, and electrostatic gating, e.g., see Refs. 4,5,10,16,20,[33][34][35]39,42,43 . Interesting properties such as gap opening 11,33,34,43 , appearing degenerate zero-energy edge states 4,10 , magnetic and ferromagnetic ordering 10,29 , long-spin relaxation time 10 , and realization of tunable multidot systems 44 , have been reported in these studies.…”

“…The electronic properties of untwisted AB-or AA-stacked BLG QDs have been studied both theoretically 11,16,38,41,42 and experimentally 15,17 . In a tBLG QD, twist angle can be used as a new knob to tune the electronic properties of the system.…”