A simple model of Coulomb disorder and screening in graphene

Abstract

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 two-dimensional concentration $n_0 \sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0 \sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.