Simple model of Coulomb disorder and screening in graphene

We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration N/2 in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates the two-dimensional concentrations n0 ∼ N2/3 of electrons and holes in the graphene sample. Electrons and holes reside in alternating in space puddles of the size R0 ∼ N-1/3. A typical puddle has only one or two carriers in qualitative agreement with the recent scanning single electron transistor experiment.