Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization

TL;DR

This paper investigates how disorder-induced impurity states in graphene influence quantum Hall effects, revealing critical states and unconventional conductance phenomena through large-scale real-space transport simulations.

Contribution

It introduces a detailed analysis of impurity state percolation and its impact on Hall conductance in disordered graphene, explaining previously unexplained experimental anomalies.

Findings

Identification of magnetic-field dependent impurity states causing Hall conductance anomalies

Demonstration of percolation of impurity states at critical energies

Correlation between defect density, system size, and transport properties

Abstract

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 bandgap 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.