Anderson Transition in Disordered Graphene

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).

4 pages

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Cited by in corpus (4)

• RKKY Interactions in Graphene: Dependence on Disorder and Gate Voltage
• Analytical and numerical study of uncorrelated disorder on a honeycomb lattice
• The effects of disorder and interactions on the Anderson transition in doped Graphene
• Anderson Transition in Disordered Bilayer Graphene