A simple model of Coulomb disorder and screening in graphene

TL;DR

This paper presents a simple model for Coulomb disorder in graphene, showing how randomly distributed charged centers induce electron-hole puddles with specific size and concentration, aligning with experimental observations.

Contribution

The model introduces a straightforward approach to understanding Coulomb disorder and screening effects in graphene, predicting puddle size and carrier concentration.

Findings

Electron-hole puddles of size R_0 ~ N^{-1/3}

Puddles contain one or two carriers

Carrier concentration n_0 ~ N^{2/3}

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.