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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Chiral tunnelling and the Klein paradox in graphene

From Wikipedia, the free encyclopedia. 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.

These results were expanded to higher dimensions, and kleiin other types of potentials, such as a linear step, a square barrier, a smooth potential, etc.

Green lines in Fig. This section needs expansion. By using this site, you agree to the Terms of Use and Privacy Policy. This article needs attention from an expert in physics. Many experiments in electron transport in graphene rely on the Klein paradox for massless particles.

Negative Refraction for Electrons? The specific problem is: Both the incoming and transmitted wave functions are associated with positive group velocity Blue lines in Fig. Moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted. Articles needing expert attention All articles needing expert attention Physics ln needing expert attention Articles to be expanded from May All articles to be expanded Articles using small message boxes.


The meaning of this paradox was intensely debated at the time.

Chiral tunnelling and the Klein paradox in graphene Author s: We now want to calculate the transmission and reflection coefficients, TR. Inphysicist Oskar Klein [1] obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. Some chirla of this site may not work without it. Please use this identifier to cite or link to this item: This explanation best suits the single particle solution cited above.

The transmission coefficient is always larger than zero, and approaches 1 as the potential step goes to infinity.

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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 existence of particle—antiparticle pairs at the potential. Retrieved from ” https: Here we show that the effect can be tested in a conceptually simple condensed-matter experiment using electrostatic barriers in single- and kleij graphene. This strategy was also applied to obtain analytic solutions to the Dirac equation for an infinite square well.

Owing to fhe chiral nature of their quasiparticles, quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, non-relativistic electrons.

[cond-mat/] Chiral tunneling and the Klein paradox in graphene

Views Read Edit View history. 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. You can help by adding to it. 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.


WikiProject Physics may paradod able to help recruit an expert. For the massive case, the calculations are similar to the above. The phenomenon is discussed in many contexts in particle, nuclear and astro-physics tunndlling direct tests of the Klein paradox using elementary particles have so far proved impossible. JavaScript is disabled for your browser.

The paradox presented a quantum mechanical objection to the notion of an electron confined within a nucleus.

This page was last edited on 31 Mayat Chiral tunnelling and the Klein paradox in graphene. 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.

The results are as surprising as in the massless case. One interpretation of the paradox is that a potential step cannot reverse the direction of the group velocity of a massless relativistic particle.

Fulltext present in this item. The diagrams and interpretation presented here need confirmation.

In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping.