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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Klein paradox

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. The specific problem is: Green lines in Fig.

This section needs expansion. For the massive case, the calculations are similar to the above.

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Some features of this site may not work without it. 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 WikiProject Physics may be able to help recruit an expert. JavaScript is disabled for your browser.

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. 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. The so-called Klein paradox – unimpeded penetration of relativistic particles through high and wide potential barriers – is one grahpene the most exotic and counterintuitive consequences of quantum electrodynamics. Fulltext present in this item.

One interpretation of the paradox is that a potential step cannot reverse the direction of the group velocity of a massless relativistic particle.

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

This explanation best suits the single particle solution cited above. 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 using electrostatic barriers cuiral single- and klejn graphene. 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. Moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted.

You can help by adding to it. The transmission coefficient is always larger than zero, and approaches 1 as the potential step goes to infinity. The meaning of this paradox was intensely debated at the time. From Wikipedia, the free encyclopedia. Negative Refraction for Electrons? This article needs attention from an expert in physics.

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Many experiments in klsin transport in graphene rely on the Klein paradox for massless particles. The results are as surprising as in the massless case.


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Chiral tunnelling and the Klein paradox in graphene. Retrieved from ” https: Chiral tunnelling and the Klein paradox in graphene Author klrin The immediate application ths the paradox was to Rutherford’s proton—electron model for neutral particles within the nucleus, before the discovery of the neutron.

Please use this identifier to cite or link to this item: This strategy was also applied to obtain analytic solutions to the Dirac equation for an infinite square well.

By using this site, you agree to the Terms of Use and Privacy Policy. The diagrams and interpretation presented chlral need confirmation. Other, more complex interpretations are suggested in literature, in the pararox of quantum field theory where the unrestrained tunnelling is shown to occur due to the existence of particle—antiparticle pairs at the potential.

Both the incoming and transmitted wave functions are associated with positive group velocity Blue lines in Fig. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. Views Read Edit View history.