Localization of Dirac electrons by Moire patterns in graphene bilayers

TL;DR

This paper investigates how Moire patterns in rotated graphene bilayers cause localization of Dirac electrons and significantly reduce their velocity, especially at small rotation angles, leading to localized states in AA zones.

Contribution

It combines ab initio and tight-binding methods to show velocity renormalization and electron localization due to Moire pattern coupling in graphene bilayers.

Findings

Velocity tends to zero at small rotation angles.

Electrons are localized in AA zones of the Moire pattern.

Strong velocity renormalization due to periodic coupling.

Abstract

We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.