Scaling and quantum phase transitions of disordered graphene in the quantum Hall regime.

We investigate the magneto-transport properties of disordered graphene samples in the quantum Hall (QH) regime. Despite the huge attention that the QH effect in graphene has received in the past decade, there are still open questions about the effects of the disorder on the transition states between Hall plateaus, especially regarding scaling properties. Such transition states have been intensively studied in the context of two-dimensional electron gases and found to exhibit universal scaling behavior. The situation is less clear in graphene, which displays an anomalous quantum Hall effect as a consequence of the valley degeneracy. For a sufficiently strong disorder that causes valley mixing, theoretical works have predicted Landau level splittings and even a transition to the conventional quantum Hall regime. The latter behavior has not been experimentally reported. To elucidate this issue, we address the problem by calculating the longitudinal and Hall resistances of graphene systems up to 10^5 atoms in a Hall bar geometry via the Landauer-Büttiker formalism. We consider both scalar and chiral disorder with different disorder correlation lengths. Finally, we discuss how intervalley/intravalley scatterings affect the QH transition states in graphene.