Seventy years of the Klein paradox

Dombey, Norman; Calogeracos, A.

doi:10.1016/s0370-1573(99)00023-x

Cited by 239 publications

(150 citation statements)

References 10 publications

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“…In addition, graphene quantum dots allow elucidating the quantum-to-classical crossover in both regular and chaotic-confined billiard systems with massless particles [108,156,157]. However, confining electrons in graphene is challenging, mainly due to the gapless electronic structure [4] and phenomena related to Klein tunneling [22,23]. Therefore, split gate techniques (e.g., [164]) well-known for semiconducting materials, to fabricate quantum dots are hard to apply.…”

Section: Graphene Quantum Dotsmentioning

confidence: 99%

“…This leads to unprecedented carrier mobilities of up to 40 000 cm 2 /(V·s) [16] even at room temperature or up to 200 000 to 1 000 000 cm 2 /(V·s) in suspended graphene at low temperatures [17][18][19][20], making graphene a promising material for high mobility nanoelectronic applications. Pseudo-relativistic Klein tunneling [21][22][23] and related phenomena make it hard to confine carriers by electrostatic potentials. The so-called Klein paradox [24,25] that refers to the transmission of relativistic particles through high and wide potential barriers is an exotic and counterintuitive consequence of QED [23].…”

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confidence: 99%

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Transport in graphene nanostructures

et al. 2011

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Graphene nanostructures are promising candidates for future nanoelectronics and solid-state quantum information technology. In this review we provide an overview of a number of electron transport experiments on etched graphene nanostructures. We briefly revisit the electronic properties and the transport characteristics of bulk, i.e., two-dimensional graphene. The fabrication techniques for making graphene nanostructures such as nanoribbons, single electron transistors and quantum dots, mainly based on a dry etching "paper-cutting" technique are discussed in detail. The limitations of the current fabrication technology are discussed when we outline the quantum transport properties of the nanostructured devices. In particular we focus here on transport through graphene nanoribbons and constrictions, single electron transistors as well as on graphene quantum dots including double quantum dots. These quasi-one-dimensional (nanoribbons) and quasi-zero-dimensional (quantum dots) graphene nanostructures show a clear route of how to overcome the gapless nature of graphene allowing the confinement of individual carriers and their control by lateral graphene gates and charge detectors. In particular, we emphasize that graphene quantum dots and double quantum dots are very promising systems for spin-based solid state quantum computation, since they are believed to have exceptionally long spin coherence times due to weak spin-orbit coupling and weak hyperfine interaction in graphene.

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Section: Graphene Quantum Dotsmentioning

confidence: 99%

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confidence: 99%

Transport in graphene nanostructures

et al. 2011

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“…This paradox can be resolved by assuming the B Muhammad Adeel Ajaib adeel@udel.edu 1 Department of Physics and Astronomy, Ursinus College, Collegeville, PA 19426, USA production of particle-antiparticle pairs at the barrier. Other methods have also been proposed in literature to resolve this paradox (see, for example, the list of references [3][4][5][6])…”

Section: Introductionmentioning

confidence: 99%

A Fundamental Form of the Schrodinger Equation

Ajaib

2015

Found Phys

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We propose a first order equation from which the Schrodinger equation can be derived. Matrices that obey certain properties are introduced for this purpose. We start by constructing the solutions of this equation in 1D and solve the problem of electron scattering from a step potential. We show that the sum of the spin up and down, reflection and transmission coefficients, is equal to the quantum mechanical results for this problem. Furthermore, we present a 3D version of the equation which can be used to derive the Schrodinger equation in 3D.Comment: 13 pages, 4 Figures, version to be published in FOO

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“…In this case, the transmission probability T depends only weakly on the barrier height, approaching the perfect transparency for very high barriers, in stark contrast to the conventional, nonrelativistic tunneling where T exponentially decays with increasing V 0 . This relativistic effect can be attributed to the fact that a sufficiently strong potential, being repulsive for electrons, is attractive for positrons and results in positron states inside the barrier, which align in energy with the electron continuum outside 4,5,6 . Matching between electron and positron wavefunctions across the barrier leads to the high-probability tunneling described by the Klein paradox 7 .…”

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confidence: 99%

Chiral tunnelling and the Klein paradox in graphene

2006

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The so-called Klein paradox -unimpeded penetration of relativistic particles through high and wide potential barriers -is one of the most exotic and counterintuitive consequences of quantum electrodynamics (QED). The phenomenon is discussed in many contexts in particle, nuclear and astro-physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment by using electrostatic barriers in single-and bi-layer graphene. Due to the chiral nature of their quasiparticles, quantum tunneling in these materials becomes highly anisotropic, qualitatively different from the case of normal, nonrelativistic electrons.Massless Dirac fermions in graphene allow a close realization of Klein's gedanken experiment whereas massive chiral fermions in bilayer graphene offer an interesting complementary system that elucidates the basic physics involved.

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Seventy years of the Klein paradox

Cited by 239 publications

References 10 publications

Transport in graphene nanostructures

Transport in graphene nanostructures

A Fundamental Form of the Schrodinger Equation

Chiral tunnelling and the Klein paradox in graphene

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