Anomalous localization and quantum Hall effect in disordered graphene

Pavel Ostrovsky

Forschungszentrum Karlsruhe, Germany

Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This gives rise to a number of unusual physical properties of this system distinguishing it from conventional two-dimensional metals. Among remarkable properties of graphene are apparent absence of localization and anomalous quantum Hall effect. In the present work we study effects of disorder on the transport of two-dimensional massless Dirac fermions. Specifically, we consider anomalies of the quantum Hall effect, conductivity at the Dirac point in the absence of magnetic field, and ballistic electron propagation in a short disordered graphene strip. All these phenomena depend strongly on the character of disorder. It is only special symmetries of disorder that give rise to the anomalous quantum Hall effects and the absence of localization in graphene. We analyze the symmetries of single- and double-layer graphene in magnetic field and identify the conditions for unconventional Hall quantization. In zero magnetic field (symplectic symmetry), we reveal peculiar topological properties of Dirac fermions preventing them from localization. We also analyze the phase diagram of the system taking into account electron-electron interaction. The study of ballistic transport in short graphene samples sheds light on the establishment of unusual transport properties and relates our findings with the results of recent experiments.