L\'evy flights due to anisotropic disorder in graphene

TL;DR

This paper investigates how anisotropic impurity distributions in graphene create stripe states that enable Le9vy-flight transport, significantly increasing conductivity along certain directions, contrasting with localized states in fully random impurity scenarios.

Contribution

It introduces a model of anisotropic impurity placement in graphene that leads to stripe states and Le9vy-flight transport, supported by numerical and analytical methods.

Findings

Stripe states suppress back-scattering in the impurity lines.

Conductivity along stripe direction increases with the square root of system length.

Anisotropic disorder enhances conductivity near the Dirac point, unlike random impurities.

Abstract

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed back-scattering are formed in this model in the direction of the lines. The system reveals L\'evy-flight transport in stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent $T$-matrix approximation.