Quantum Hall effect in graphene: Disorder effect and phase diagram

We numerically study the quantum Hall effect (QHE) in graphene based on a lattice model in the presence of disorder. Two distinct QHE regimes are identified in the energy band with unconventional ``half-integer'' QHE appearing near the band center, in agreement with the experimental observation. A topological invariant Chern number description provides a consistent understanding of the peculiar behavior of the two QHE regimes in the energy band. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is through the float-up of extended levels towards the band center. An insulating phase emerges between $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}2$ QHE plateaus at the band center in weak disorder region, which may explain the experimentally observed resistance discontinuity near zero gate voltage.