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

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 Author Schweitzer, L. ♦ Markos, P. Source arXiv.org Content type Text File Format PDF Date of Submission 2008-07-21 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics Subject Keyword Condensed Matter - Mesoscale and Nanoscale Physics ♦ Condensed Matter - Disordered Systems and Neural Networks ♦ physics:cond-mat 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 $\alpha(0)=2.14\pm 0.02$. Description Reference: Phys. Rev. B 78, 205419 (2008) Educational Use Research Learning Resource Type Article