Klein tunneling in graphene: optics with massless electrons

TL;DR

This paper reviews Klein tunneling in graphene, highlighting its optical analogies, the role of pseudo-spin conservation, and discussing experimental observations and differences between mono- and bi-layer graphene.

Contribution

It provides a pedagogical overview connecting Klein tunneling in graphene to optical phenomena and clarifies misconceptions about quantum tunneling effects.

Findings

Klein tunneling in graphene is analogous to optical refraction phenomena.

Conservation of pseudo-spin prevents backscattering at normal incidence.

Experimental status of Klein tunneling in graphene is comprehensively reviewed.

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-P\'erot 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.