Eur. Phys. J. B 83, 301-317 (2011)
https://doi.org/10.1140/epjb/e2011-20351-3

Colloquium

Klein tunneling in graphene: optics with massless electrons

¹ Institut d’Électronique Fondamentale, Univ. Paris-Sud, CNRS UMR 8622, 91405 Orsay, France
² Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, 91405 Orsay, France

^a e-mail: fuchs@lps.u-psud.fr

Received: 6 May 2011
Received in final form: 17 August 2011
Published online: 10 October 2011

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.