Chiral tunneling in single and bilayer graphene

TL;DR

This paper reviews chiral tunneling phenomena in single and bilayer graphene, providing a semiclassical theory incorporating Berry phase, and offers analytical formulas validated by numerical results, highlighting unique transmission properties in graphene junctions.

Contribution

It introduces a semiclassical framework for chiral tunneling in graphene, including Berry phase effects, and derives analytical formulas for tunneling behavior.

Findings

Total transmission at normal incidence in asymmetric n-p-n junctions

Side resonances are suppressed in these junctions

Analytical formulas agree with numerical simulations

Abstract

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