Klein paradox for a pn junction in multilayer graphene

TL;DR

This paper investigates Klein and anti-Klein tunneling phenomena in multilayer graphene, deriving formulas for tunneling angles and analyzing how stacking order affects charge carrier behavior.

Contribution

It introduces an algebraic formula for tunneling angles in multilayer graphene and decomposes complex stacking into simpler pseudospin doublets, advancing understanding of charge transport.

Findings

Klein and anti-Klein tunneling occur in multilayer graphene.

Derived algebraic formula predicts tunneling angles.

Decomposition into pseudospin doublets simplifies multilayer analysis.

Abstract

Charge carriers in single and multilayered graphene systems behave as chiral particles due to the particular lattice symmetry of the crystal. We show that the interplay between the meta-material properties of graphene multilayers and the pseudospinorial properties of the charge carriers result in the occurrence of Klein and anti-Klein tunneling for rhombohedral stacked multilayers. We derive an algebraic formula predicting the angles at which these phenomena occur and support this with numerical calculations for systems up to four layers. We present a decomposition of an arbitrarily stacked multilayer into pseudospin doublets that have the same properties as rhombohedral systems with a lower number of layers.