PDF | The so-called Klein paradox-unimpeded penetration of relativistic particles through high and wide potential barriers-is one of the most. This plot shows the transmission coefficient for a barrier of height in graphene as a function of the angle of a plane wave incident on the barrier. Title: Chiral tunnelling and the Klein paradox in graphene. Author(s): Katsnelson, M.I. ; Novoselov, K.S. ; Geim, A.K.. Publication year: Source: Nature.

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This page was last edited on 31 Mayat Views Read Edit View history. These results were expanded to higher dimensions, and to other types of potentials, such as a linear step, a square barrier, a smooth potential, etc. The diagrams and interpretation presented here need confirmation. Moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted. The meaning of this paradox was intensely debated at the time.

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The transmission coefficient is always larger than zero, and approaches 1 as the potential step goes to infinity. Articles needing expert attention All articles needing expert attention Physics articles needing expert attention Articles to be expanded from May All articles to be expanded Articles using small message boxes.

By using this site, you agree to the Terms of Use and Privacy Policy. We now want to calculate the transmission and reflection coefficients, TR.

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Please use this identifier to cite or link to this item: Here we show that the effect can be tested in a conceptually simple condensed-matter experiment using electrostatic barriers in single- and bi-layer graphene. The paradox presented a quantum mechanical objection to the notion of an electron confined within a nucleus. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping.


One interpretation of the paradox is that a potential step cannot reverse the direction of the group velocity of a massless relativistic particle. This strategy was also applied to obtain traphene solutions to the Dirac equation for an infinite square well.

Chiral tunnelling and the Klein paradox in graphene. This article needs attention from an expert in physics. 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.

Klein paradox

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Other, more complex interpretations are suggested in literature, in the context of quantum field theory where the unrestrained tunnelling is shown to occur due to the ggraphene of particle—antiparticle pairs at the potential. Chiral tunnelling and the Klein paradox in graphene Author s: JavaScript is disabled for your browser.

Retrieved from ” https: Many experiments in electron transport in graphene rely on the Klein paradox for massless particles. This item appears in the following Collection s Faculty of Science [] Open Access publications [] Freely accessible full text publications Electronic publications [] Freely accessible full text publications plus those not yet available due to embargo Academic publications [] Academic output Radboud University.


Owing to the chiral nature of their quasiparticles, quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, non-relativistic electrons. The results are as surprising as in the massless case.

Chiral Tunneling and the Klein Paradox in Graphene – Wolfram Demonstrations Project

The immediate application of the paradox was to Rutherford’s proton—electron model for neutral particles within the nucleus, before the discovery of the neutron.

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.

For the massive case, the calculations are similar to the above. Negative Refraction for Electrons?

The specific problem is: The phenomenon is discussed in many contexts in particle, nuclear and astro-physics but direct paradoz of the Klein paradox using elementary particles have so far proved impossible. Inphysicist Oskar Klein [1] obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier.

Rutgers University Department of Physics and Astronomy

Both cihral incoming and transmitted wave functions are associated with positive group velocity Blue lines in Fig. Green lines in Fig. This explanation best suits the single particle solution cited above. From Wikipedia, the free encyclopedia.