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Chiral tunnelling and the Klein paradox in graphene


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. 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 in single- and bi-layer graphene. 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. 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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Figure 1: Tunnelling through a potential barrier in graphene.
Figure 2: Klein-like quantum tunnelling in graphene systems.
Figure 3: Chiral versus non-chiral tunnelling.
Figure 4: The chiral nature of quasiparticles in graphene strongly affects its transport properties.


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We are grateful to A. C. Neto, V. Fal’ko, P. Guinea and D. Khveshchenko for illuminating discussions. This work was supported by EPSRC (UK) and FOM (Netherlands).

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Correspondence to M. I. Katsnelson or A. K. Geim.

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Katsnelson, M., Novoselov, K. & Geim, A. Chiral tunnelling and the Klein paradox in graphene. Nature Phys 2, 620–625 (2006).

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