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

References in corpus (12)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• Substrate-induced band gap opening in epitaxial graphene
• The Kernel Polynomial Method
• Modeling disorder in graphene
• Topological delocalization of two-dimensional massless Dirac fermions
• Adsorbate-limited conductivity of graphene
• Origin of the energy bandgap in epitaxial graphene
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Anderson localization of electron states in graphene in different types of disorder
• Transport regimes in surface disordered graphene sheets