Anderson Transition in Disordered Graphene

TL;DR

This paper investigates how disorder affects electronic states in graphene, revealing a transition from extended to localized states and identifying a mobility edge, challenging traditional 2D localization theory.

Contribution

It introduces the use of the regularized kernel polynomial method to study large disordered graphene lattices, demonstrating a disorder-induced Anderson transition.

Findings

Weak disorder preserves extended Dirac fermions with reduced velocities

Strong disorder induces a mobility edge separating localized and extended states

Contradicts the scaling theory predicting all states are localized in 2D

Abstract

We use the regularized kernel polynomial method (RKPM) to numerically study the effect disorder on a single layer of graphene. This accurate numerical method enables us to study very large lattices with millions of sites, and hence is almost free of finite size errors. Within this approach, both weak and strong disorder regimes are handled on the same footing. We study the tight-binding model with on-site disorder, on the honeycomb lattice. We find that in the weak disorder regime, the Dirac fermions remain extended and their velocities decrease as the disorder strength is increased. However, if the disorder is strong enough, there will be a {\em mobility edge} separating {\em localized states around the Fermi point}, from the remaining extended states. This is in contrast to the scaling theory of localization which predicts that all states are localized in two-dimensions (2D).