Abstract
In this paper, we review chiral (Klein) tunneling in single-layer and bilayer graphene and present its semiclassical theory, including the Berry phase and the Maslov index. The peculiarities of chiral tunneling are naturally explained in terms of the classical phase space. In one-dimensional geometry, we reduced the original Dirac equation, describing the dynamics of charge carriers in single-layer graphene, to an effective Schrödinger equation with a complex potential. This allowed us to study tunneling in detail and obtain analytical formulae. Our predictions are compared with numerical results. We have also demonstrated that for the case of an asymmetric n–p–n junction in single-layer graphene, there is total transmission only for normal incidence; side resonances are suppressed.
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