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The so-called Klein paradox - unimpeded penetration of relativistic particlesthrough high and wide potential barriers - is one of the most exotic andcounterintuitive consequences of quantum electrodynamics (QED). The phenomenonis discussed in many contexts in particle, nuclear and astro- physics butdirect tests of the Klein paradox using elementary particles have so far provedimpossible. Here we show that the effect can be tested in a conceptually simplecondensed-matter experiment by using electrostatic barriers in single- andbi-layer graphene. Due to the chiral nature of their quasiparticles, quantumtunneling in these materials becomes highly anisotropic, qualitativelydifferent from the case of normal, nonrelativistic electrons. Massless Diracfermions in graphene allow a close realization of Klein's gedanken experimentwhereas massive chiral fermions in bilayer graphene offer an interestingcomplementary system that elucidates the basic physics involved.Comment: 15 pages, 4 figure

Chiral tunnelling and the Klein paradox in graphene