Dirac electron scattering from a cluster of electrostatically defined quantum dots in graphene

Sadrara, Mahdiyeh; Miri, MirFaez

doi:10.1103/physrevb.99.155432

Cited by 11 publications

(4 citation statements)

References 39 publications

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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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Section: Introductionmentioning

confidence: 91%

Energy spectra of graphene quantum dots induced between Landau levels

Giavaras

2021

Preprint

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“…It turns out that eigenfunctions of H 0 with energy E 0 = hv F k 0 can be written as J m (k 0 r)e imθ (1, 0) T ± iJ m+1 (k 0 r)e i(m+1)θ (0, 1) T , where J m (u) is either the Hankel function of the first kind H (1) m (u) ≡ J m (u) + iY m (u), the Bessel function J m (u), or the Neumann function Y m (u). To properly describe the multiple scattering of electrons from quantum dots, we expand the incident wave ψ inc , the waves ψ core,l and ψ shell,l transmitted into the core and shell of the lth quantum dot, and the scattered wave ψ sca , in terms of the simultaneous eigenfunctions of H 0 and J z , and relate the expansion of the transmitted and scattered waves to that of the incident wave [38].…”

Section: Dirac Electron Scatteringmentioning

confidence: 99%

“…Guided by the generalized multiparticle Mie theory [37], the Dirac electron scattering from a cluster of quantum dots-in the context of the Klein tunneling suppression, asymmetric scattering pattern, and Fano resonances-is addressed [38]. In this paper, we study cloaking of a cluster of gatedefined core-shell quantum dots in graphene.…”

Section: Introductionmentioning

confidence: 99%

Collective cloaking of a cluster of electrostatically defined core–shell quantum dots in graphene

Sadrara

Miri

2022

J. Phys.: Condens. Matter

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We study cloaking of a cluster of electrostatically deﬁned core-shell quantum dots in graphene. Guided by the generalized multiparticle Mie theory, the Dirac electron scattering from a cluster of quantum dots is addressed. Indeed distant quantum dots may experience a sort of individual cloaking. But despite the multiple scattering of an incident electron from a set of adjacent quantum dots, collective cloaking may happen. Via a proper choice of the radii and bias voltages of shells, two most important scattering coeﬃcients and hence the scattering eﬃciency of the cluster dramatically decrease. Energy-selective electron cloaks are realizable. More importantly, clusters simultaneously transparent to electrons of diﬀerent energies, are achievable. Being quite sensitive to applied bias voltages, clusters of core-shell quantum dots may be used to develop switches with high on-oﬀ ratios.

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“…[1], which presented an experimental demonstration of an electronic analogue of Mie scattering by using a graphene superlattice as a conductor imbibed into a regular EQDC array. They were followed by other relevant work on the effect of circular electrostatic potentials in graphene [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition

Fonseca¹,

Pereira²,

Barbosa³

2023

Preprint

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In this work we propose an electronic Lévy flight device, analogous to a recent optical realization. To that end, we investigate the transmission of electrons in graphene nanoribbons in the presence of circular electrostatic clusters, whose diameter follow a power-law distribution. We analyze the effect of the electrostatic clusters on the electronic transport regime of the nanoribbons, in terms of its diffusion behavior. Our numerical calculations show that the presence of circular electrostatic clusters induces a transition from Lévy (superdiffusive) to diffusive transport as the energy increases. Furthermore, we argue that in our electronic Lévy flight device, superdiffusive transport is an exclusive feature of the low-energy quantum regime, while diffusive transport is a feature of the semiclassical regime. Therefore, we attribute the observed transition to the chiral symmetry breaking, once the energy moves away from the Dirac point of graphene.

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Dirac electron scattering from a cluster of electrostatically defined quantum dots in graphene

Cited by 11 publications

References 39 publications

Energy spectra of graphene quantum dots induced between Landau levels

Energy spectra of graphene quantum dots induced between Landau levels

Collective cloaking of a cluster of electrostatically defined core–shell quantum dots in graphene

A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition

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