Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy band gap and Landau-level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large-size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size, and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-field-dependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum-transport anomalies reported experimentally. ; This research is partly funded by the European Union Seventh Framework Programme under Grant No. 604391 Graphene Flagship. ICN2 acknowledges support from the Severo Ochoa Program (MINECO, Grant No. SEV-2013-0295). F.O. would like to thank the Deutsche Forschungsgemeinschaft for financial support (Grant No. OR 349/1-1). ; Peer Reviewed