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

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 ν≈2.5 for the quantum Hall states but ν=0.33±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[α(s)] distribution with α(0)=2.27±0.02. In the absence of the constant magnetic field, the chiral critical state is determined by α(0)=2.14±0.02.