Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene

TL;DR

This paper investigates how incommensurability affects electron localization in twisted bilayer graphene at small angles, revealing sub-ballistic states and their impact on electronic transport in the narrow-band regime.

Contribution

It demonstrates that incommensurability induces sub-ballistic states in twisted bilayer graphene, highlighting the importance of considering incommensurate effects for accurate modeling.

Findings

Sub-ballistic states exist in the narrow-band region around the magic angle.

Incommensurability leads to delocalization in momentum space and non-Poissonian level statistics.

Conductance decreases with system size in the sub-ballistic regime for incommensurate angles.

Abstract

We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance decreases with system size for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.