Variational calculations on the energy levels of graphene quantum antidots

Kandemir, B. S.; Omer, G.

doi:10.1140/epjb/e2013-40193-1

Cited by 7 publications

(3 citation statements)

References 45 publications

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“…Several strategies for introducing a band gap have been proposed, including graphene nanoribbons (GNRs) [7][8][9], gated bilayer graphene [10] and periodic gating [11]. Alternatively, an energy gap may be created using graphene quantum dots, or graphene nanodisks, which also show promising results as hosts for spin qubits [12][13][14][15]. Another method is to introduce perforations in a periodic pattern, called a graphene antidot lattice (GAL) [16,17].…”

Section: Introductionmentioning

confidence: 99%

Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

Brun

Thomsen

Pedersen

2014

J. Phys.: Condens. Matter

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Abstract. The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation (DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an approximation of the band gap using the DE is presented. The Dirac model is compared with nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended zigzag regions give rise to localized edge states, whereas armchair edges do not. We find that the Dirac model is in quantitative agreement with TB for GALs without edge states, but deviates for antidots with large zigzag regions.

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Section: Introductionmentioning

confidence: 99%

Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

Brun

Thomsen

Pedersen

2014

J. Phys.: Condens. Matter

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“…By the presented rigorous analysis, the work also contributes to the series of the recent papers where the spectral properties of Dirac operators were discussed [55], [56], [57], [58], [59], or [60]. In particular, let us mention [61] where the variational principle was utilized for analysis of the bound states in the quantum anti-dots.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Qualitative analysis of trapped Dirac fermions in graphene

Jakubský

Krejčiřı́k

2014

Annals of Physics

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We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.Comment: 17 pages, analysis of the systems with the non-vanishing mass correcte

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“…This property offers a superior control over the dot states compared to dot states formed in nano-sheets of graphene. 6 The results are relevant to other confined systems formed in two-dimensional materials by external fields, [16][17][18][19][20][21][22][23][24][25] as well as to general hybrid graphene-based systems including defects and heterostructures. [26][27][28][29][30][31][32][33] Section II presents the physical model of the graphene quantum dot and explains with some qualitative arguments how the discrete levels of the dot emerge from the bulk Lan-dau levels.…”

Section: Introductionmentioning

confidence: 91%

Energy spectra of graphene quantum dots induced between Landau levels

Giavaras

2021

Preprint

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When an energy gap is induced in monolayer graphene the valley degeneracy is broken and the energy spectrum of a confined system such as a quantum dot, becomes rather complex exhibiting many irregular level crossings and small energy spacings which are very sensitive to the applied magnetic field. Here we study the energy spectrum of a graphene quantum dot that is formed between Landau levels, and show that for the appropriate potential well the dot energy spectrum in the first Landau gap can have a simple pattern with energies coming from one of the two valleys only. This part of the spectrum has no crossings, has specific angular momentum numbers, and the energy spacing can be large enough, consequently, it can be probed with standard spectroscopic techniques. The magnetic field dependence of the dot levels as well as the effect of the massinduced energy gap are examined, and some regimes leading to a controllable quantum dot are specified. At high magnetic fields and negative angular momentum a simple approximate method to the Dirac equation is developed which gives further insight into the physics. The approximate energies exhibit the correct trends and agree well with the exact energies.

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Variational calculations on the energy levels of graphene quantum antidots

Cited by 7 publications

References 45 publications

Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

Qualitative analysis of trapped Dirac fermions in graphene

Energy spectra of graphene quantum dots induced between Landau levels

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