Klein tunneling in graphene: optics with massless electrons |
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Authors: | P E Allain and J N Fuchs |
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Institution: | (1) Department of Physics, College of Sciences, Shanghai University, Shanghai, 200444, China |
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Abstract: | This article provides a pedagogical review on Klein tunneling in graphene, i.e. the
peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two
simple situations in detail: a massless Dirac electron incident either on a potential step
or on a potential barrier and use elementary quantum wave mechanics to obtain the
transmission probability. We emphasize the connection to related phenomena in optics, such
as the Snell-Descartes law of refraction, total internal reflection, Fabry-Pérot
resonances, negative refraction index materials (the so called meta-materials), etc. We
also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not
necessarily involve passing through a classically forbidden region via evanescent waves. A
crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin,
which is discussed in detail. A major consequence is the absence of backscattering at
normal incidence, of which we give a new shorten proof. The current experimental status is
also thoroughly reviewed. The Appendix contains the discussion of a one-dimensional toy
model that clearly illustrates the difference in Klein tunneling between mono- and
bi-layer graphene. |
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Keywords: | |
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