Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Abstract

The electronic properties of a bricklayer model, which shares the same topology as the hexagonal lattice of graphene, are investigated numerically. We study the influence of random magnetic-field disorder in addition to a strong perpendicular magnetic field. We found a disorder-driven splitting of the longitudinal conductance peak within the narrow lowest Landau band near the Dirac point. The energy splitting follows a relation which is proportional to the square root of the magnetic field and linear in the disorder strength. We calculate the scale invariant peaks of the two-terminal conductance and obtain the critical exponents as well as the multifractal properties of the chiral and quantum Hall states. We found approximate values $\nu \approx 2.5$ for the quantum Hall states, but $\nu =0.33\pm 0.1$ for the divergence of the correlation length of the chiral state at E=0 in the presence of a strong magnetic field. Within the central $n=0$ Landau band, the multifractal properties of both the chiral and the split quantum Hall states are the same, showing a parabolic $f[\alpha (s)]$ distribution with $\alpha (0)=2.27\pm 0.02$. In the absence of the constant magnetic field, the chiral critical state is determined by $\alpha (0)=2.14\pm 0.02$.

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Cited by in corpus (14)

• Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene
• Quantum Hall plateau transition in graphene with spatially correlated random hopping
• Electric transport through circular graphene quantum dots: Presence of disorder
• Energy gap in graphene nanoribbons with structured external electric potentials
• Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties
• Metal-insulator transition in a 2D system of chiral unitary class
• Splitting of critical energies in the $n$=0 Landau level of graphene
• Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders
• Disordered two-dimensional electron systems with chiral symmetry
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Narrow depression in the density of states at the Dirac point in disordered graphene
• Scaling at chiral quantum critical points in two dimensions
• Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices
• Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level