The effect of strong long-range disorder on the quantization of the Hall conductivity ${\sigma }_{xy}$ in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in ${\sigma }_{xy}$ except the plateaus at ${\sigma }_{xy}=\mp e^2/2h$ (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.

• Received 20 January 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.246806