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

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

2008-07-21

arxiv.org/abs/0807.3245v3

Phys. Rev. B 78, 205419 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1103/PhysRevB.78.205419

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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