Abstract
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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