Analytical study of the energy levels in bilayer graphene quantum dots

Costa, D. R. da; Zarenia, M.; Chaves, Andrey; Farias, G. A.; Peeters, F. M.

doi:10.1016/j.carbon.2014.06.078

Cited by 45 publications

(45 citation statements)

References 41 publications

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“…We notice that, like the case of monolayer [19] and AB-stacked bilayer graphene [29], the electron energy presents a minimum for a particular value of the angular momentum m. The minimum energy for B = −3T is given by two values of m: m = 20 and m = −10. However, the minimum energy for B = 0T and B = 3T, are respectively, given by m = 15, −16 and m = 9, −21.…”

Section: Resultsmentioning

confidence: 64%

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

Zahidi

Belouad

Jellal

2017

Mater. Res. Express

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We theoretically analyze the energy spectrum of a quantum ring in AA-stacked bilayer graphene with radius R for a zero width subjected to a perpendicular magnetic field B. An analytical approach, using the Dirac equation, is implemented to obtain the energy spectrum by freezing out the carrier radial motion. The obtained spectrum exhibits different symmetries and for a fixed total angular momentum m, it has a hyperbolic dependence of the magnetic field. In particular, the energy spectra are not invariant under the transformation B −→ −B. The application of a potential, on the upper and lower layer, allows to open a gap in the energy spectrum and the application of a non zero magnetic field breaks all symmetries. We also analyze the basics features of the energy spectrum to show the main similarities and differences with respect to ideal quantum ring in monolayer, AB-stacked bilayer graphene and a quantum ring with finite width in AB-stacked bilayer graphene.

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Section: Resultsmentioning

confidence: 64%

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

Zahidi

Belouad

Jellal

2017

Mater. Res. Express

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“…In an AB-stacked BLG, the atoms in the A (B) sublattice in the bottom layer are linked with B (A) atoms in the top layer. M i and V i are the on-site mass potential term and the on-site electrostatic potential, respectively, used to open a gap in the energy spectrum of BLG and, consequently, to simulate electronic confinement in BLG nanostructures [32,33]. The staggered site-dependent potential is defined in such a way that M i = M 0 (M i = −M 0 ) if i belongs to the lattice A (B) in one layer and B (A) in the other one [33].…”

Section: Methodsmentioning

confidence: 99%

“…This leads to an inversion asymmetry between the layers and opens an energy gap in the energy spectrum. Tailoring the gap, by using applied gate potentials, leads to the creation of electrostatic confined QDs in BLG, as has been experimentally [21,24,25] and theoretically [26][27][28][29][30][31][32][33][34] reported in the literature. The energy spectra of such QDs are not determined by the type of edges or the disorder present at the edges.…”

Section: Introductionmentioning

confidence: 95%

Magnetic field dependence of energy levels in biased bilayer graphene quantum dots

et al. 2016

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Using the tight-binding approach, we study the influence of a perpendicular magnetic field on the energy levels of hexagonal, triangular, and circular bilayer graphene (BLG) quantum dots (QDs) with zigzag and armchair edges. We obtain the energy levels for AB (Bernal)-stacked BLG QDs in both the absence and the presence of a perpendicular electric field (i.e., biased BLG QDs). We find different regions in the spectrum of biased QDs with respect to the crossing point between the lowest-electron and-hole Landau levels of a biased BLG sheet. Those different regions correspond to electron states that are localized at the center, edge, or corner of the BLG QD. Quantum Hall corner states are found to be absent in circular BLG QDs. The spatial symmetry of the carrier density distribution is related to the symmetry of the confinement potential, the position of zigzag edges, and the presence or absence of interlayer inversion symmetry.

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“…From a theoretical perspective this calls for a quantitative understanding of the electronic properties and their size dependence. There exist several studies based on an effective Dirac Hamiltonian with suitable boundary conditions , though there is ambiguity about the exact boundary treatment . Besides a lack of quantitative insight, one major drawback of this analytical approach is that it does not account for the structural relaxation at edges, which is known to play a significant role for the electronic properties .…”

Section: Introductionmentioning

confidence: 99%

Hexagonal graphene quantum dots

Ghosh

Schwingenschlögl

2016

Physica Rapid Research Ltrs

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We study hexagonal graphene quantum dots, using density functional theory, to obtain a quantitative description of the electronic properties and their size dependence, considering disk and ring geometries with both armchair and zigzag edges. We show that the electronic properties of quantum dots with armchair edges are more sensitive to structural details than those with zigzag edges. As functions of the inner and outer radii, we find in the case of armchair edges that the size of the band gap follows distinct branches, while in the case of zigzag edges it changes monotonically. This behaviour is further analyzed by studying the ground state wave function and explained in terms of its localisation. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

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Analytical study of the energy levels in bilayer graphene quantum dots

Cited by 45 publications

References 41 publications

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

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

Magnetic field dependence of energy levels in biased bilayer graphene quantum dots

Hexagonal graphene quantum dots

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