Theory of anomalous quantum Hall effects in graphene

We develop a theory of anomalous quantum Hall effects in graphene. We demonstrate that the Landau level structure by itself is not sufficient to determine the form of the quantum Hall effect. It is only a special symmetry of disorder that gives rise to anomalous quantization of Hall conductivity in graphene. We analyze the. symmetries of disordered single- and double-layer graphene samples in magnetic field and identify the conditions for anomalous Hall quantization.