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We investigate, analytically and numerically, the effects of disorder on thedensity of states and on the localization properties of the relativistic twodimensional fermions in the lowest Landau level. Employing a supersymmetrictechnique, we calculate the exact density of states for the Cauchy (Lorentzian)distribution for various types of disorders. We use a numerical technique toestablish the localization-delocalization (LD) transition in the lowest Landaulevel. For some types of disorder the LD transition is shown to belong to adifferent universality class, as compared to the corresponding nonrelativisticproblem. The results are relevant to the integer quantum Hall plateautransitions observed in graphene.

Quantum Hall plateau transition in the lowest Landau level of disordered graphene