Gate-tunable graphene quantum dot and Dirac oscillator

Belouad, Abdelhadi; Jellal, Ahmed; Zahidi, Youness

doi:10.1016/j.physleta.2015.11.025

Cited by 21 publications

(12 citation statements)

References 36 publications

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“…Recently, alternative strategies have been proposed to confine charged particles by using thin single-layer graphene strips [10,11] or nonuniform magnetic fields [12]. Graphene quantum dots [11,13,14] have been recently extensively discussed theoretically as well as from the experimental side [15][16][17][18][19][20]. It have been studied as potential hosts for spin qubits [21,22], single gatedefined dots [23].…”

Section: Introductionmentioning

confidence: 99%

Electron scattering in gapped graphene quantum dots

Belouad¹,

Zahidi²,

Jellal³

et al. 2018

EPL

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Due to Klein tunneling in graphene only quasi-bound states are realized in graphene quantum dots by electrostatic gating. Particles in the quasi-bound states are trapped inside the dot for a finite time and they keep bouncing back and forth till they find their way out. Here we study the effect of an induced gap on the scattering problem of Dirac electrons on a circular electrostatically confined quantum dot. Introducing an energy gap inside the quantum dot enables us to distinguish three scattering regimes instead of two in the case of gapless graphene quantum dot. We will focus on these regimes and analyze the scattering efficiency as a function of the electron energy, the dot radius and the energy gap. Moreover, we will discuss how the system parameters can affect the scattering resonances inside the dot.

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Section: Introductionmentioning

confidence: 99%

Electron scattering in gapped graphene quantum dots

Belouad¹,

Zahidi²,

Jellal³

et al. 2018

EPL

Self Cite

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“…Since that the relativistic version of the quantum harmonic oscillator (QHO) for spin-1/2 particles was formulated in the literature in 1989 by M. Moshinsky and A. Szczepaniak, the so-called Dirac oscillator (DO) [1], several works on this model have been and continue being performed in different areas of physics, such as in thermodynamics [2,3], nuclear physics [4][5][6], quantum chromodynamics [7,8], quantum optics [9,10], and graphene physics [11][12][13]. Besides that, the OD also is studied in other interesting physical contexts, such as in quantum phase transitions [14,15], noncommutative spaces [16,17], minimal length scenario [18,19], supersymmetry [20,21], etc.…”

Section: Introductionmentioning

confidence: 99%

Topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov–Casher effect

Oliveira

2019

Eur. Phys. J. C

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In the present paper, we investigate the influence of topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov-Casher effect. Next, we determine the two-component Dirac spinor and the relativistic energy spectrum for the bound states. We observe that this spinor is written in terms of the confluent hypergeometric functions and this spectrum explicitly depends on the quantum numbers n and m l , parameters s and η associated to the topological and spin effects, quantum phase Φ AC , and of the angular velocity Ω associated to the noninertial effects of a rotating frame. In the nonrelativistic limit, we obtain the quantum harmonic oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling. We note that the relativistic and nonrelativistic spectra grow in absolute values as functions of η, Ω, and Φ AC and its periodicities are broken due to the rotating frame. Finally, we compared our problem with other works, where we verified that our results generalizes some particular planar cases of the literature.

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“…Since it was proposed in the literature, several works on DO were carried out in different contexts. For example, in the studies of thermodynamic properties [4][5][6][7], mathematical physics [8][9][10][11][12][13], quantum chromodynamics [14,15], quantum optics [16,17], graphene physics [18][19][20][21], and so on. Recently, the first experimental realization of the onedimensional Dirac oscillator was obtained by Franco-Villafañe et al [22].…”

Section: Introductionmentioning

confidence: 99%

Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

Oliveira¹,

Maluf²,

Almeida³

2019

Annals of Physics

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In this work, we study of the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the lef thanded and right-handed projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency ω c and on the parameters Z and Φ AB that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state (n = 1) and the first excited state (n = 2). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with ω c .

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Gate-tunable graphene quantum dot and Dirac oscillator

Cited by 21 publications

References 36 publications

Electron scattering in gapped graphene quantum dots

Electron scattering in gapped graphene quantum dots

Topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov–Casher effect

Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

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