Quantum hall effect of massless dirac fermions in a vanishing magnetic field

Abstract

The effect of strong long-range disorder on the quantization of the Hall conductivity σxy in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in σxy except the plateaus at σxy= e2/2h (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. © 2008 The American Physical Society.