First Experimental Realization of the Dirac Oscillator

Franco-Villafañe, J. A.; Sadurní, E.; Barkhofen, Sonja; Kuhl, Ulrich; Mortessagne, Fabrice; Seligman, T. H.

doi:10.1103/physrevlett.111.170405

Cited by 171 publications

(169 citation statements)

References 41 publications

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“…Applying the techniques, developed to investigate the band structure of graphene 21,22 and to emulate relativistic systems 46,47 as well as molecular systems 24 , we have performed analogous experiments to study the coherent transport in graphene nanoribbons.…”

Section: A Microwave Experimentsmentioning

confidence: 99%

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

et al. 2017

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Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width 3m + 2 with integer m are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atoms of zigzag edges, broad transport gaps can be observed in all armchair ribbons as well as in rhomboid-shaped zigzag ribbons. All experimental results agree qualitatively with tight-binding calculations using the nonequilibrium Green's function method.

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Section: A Microwave Experimentsmentioning

confidence: 99%

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

et al. 2017

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“…[3,6]). Recently, the one-dimensional Dirac oscillator has had its first experimental realization [7], which made the system more attractive from the point of view of applications. The Dirac oscillator in (2 + 1) dimensions, when the third spatial coordinate is absent, has also been studied in Refs.…”

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confidence: 99%

Remarks on the Dirac oscillator in (2 + 1) dimensions

Andrade

Silva

2014

EPL

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-In this work the Dirac oscillator in (2 + 1) dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter s and angular momentum quantum number m. Contrary to earlier attempts, we show that the degeneracy of the energy spectrum can occur for all possible values of sm. In an additional analysis, we also show that an isolated bound state solution, excluded from SturmLiouville problem, exists.The Dirac oscillator, first introduced in [1] and after develop in [2], has been an usual model for studying the physical properties of physical systems in various branches of physics. In the context of theoretical contributions, the Dirac oscillator has been analyzed under different aspects such as the study of the covariance properties and FoldyWouthuysen and Cini-Touschek transformations [3], as a special case of a class of chiral solutions to the automorphism gauge field equations [4], and hidden supersymmetry produced by the interaction iM ωβr, where M is the mass, ω the frequency of the oscillator and r is the position vector, when it plays a role of anomalous magnetic interaction [5] (see also Refs. [3,6]).Recently, the one-dimensional Dirac oscillator has had its first experimental realization [7], which made the system more attractive from the point of view of applications. The Dirac oscillator in (2 + 1) dimensions, when the third spatial coordinate is absent, has also been studied in Refs. [8][9][10]. Additionally, this system was proposed in [11] to describe some electronic properties of monolayer an bylayer graphene. For a detailed approach of the Dirac oscillator see the Refs. [12,13].In this Letter, we address the Dirac oscillator in (2 + 1) dimensions. In [10], it was argued that the energy eigenvalues are degenerated only for negative values of k ϑ s, where k ϑ represents the angular momentum quantum number and s the spin projection parameter. This result, however, is not correct, as properly shown in this work. Additionally, an isolated bound state solution for the Dirac oscillator in (2 + 1) is worked out.We begin by writing the Dirac equation in (2 + 1) dimensions ( = c = 1)where p = (p x , p y ) is the momentum operator and ψ is a two-component spinor. The Dirac oscillator is obtained through the following nonminimal substitution [2]:where r = (x, y) is the position vector and ω stands for the Dirac oscillator frequency. Thus, the relevant equation isIn three dimensions the γ matrices are conveniently defined in terms of the Pauli matrices [14]where s is twice the spin value, with s = +1 for spin "up" and s = −1 for spin "down". In this manner, eq. (3) can be written aswhere π j = p j − iM ωσ z r j .p-1

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“…Pacheco et al analyzed one-dimensional Dirac oscillator in a thermal bath and they showed that its heat capacity is two times greater than that of the one-dimensional harmonic oscillator for high temperatures [2]. Franco-Villafañe et al performed the first experimental study on one-dimensional Dirac oscillator [3]. Later, Pacheco et al also studied three-dimensional Dirac oscillator in a thermal bath [4].…”

Section: Introductionmentioning

confidence: 99%

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

Lütfüoğlu¹

2018

Commun. Theor. Phys.

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In this study, we reveal the difference between Woods-Saxon (WS) and Generalized Symmetric Woods-Saxon (GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schrödinger eq. for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture.The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem, an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy, specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum.The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.

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First Experimental Realization of the Dirac Oscillator

Cited by 171 publications

References 41 publications

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

Remarks on the Dirac oscillator in (2 + 1) dimensions

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

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