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.