Mechanism for puddle formation in graphene

TL;DR

This paper investigates the formation of electron-hole puddles in graphene, revealing how bilayer graphene's puddle landscape depends solely on impurity distance, contrasting with monolayer graphene, supported by numerical analysis and experimental comparison.

Contribution

It provides a numerical demonstration of the distinct dependence of puddle landscapes in bilayer versus monolayer graphene on impurity distance.

Findings

Puddle autocorrelation in bilayer graphene depends only on impurity distance.

Quantitative agreement with experimental STM data.

Differences in puddle characteristics between monolayer and bilayer graphene.

Abstract

When graphene is close to charge neutrality, its energy landscape is highly inhomogeneous, forming a sea of electron-like and hole-like puddles, which determine the properties of graphene at low carrier density. However, the details of the puddle formation have remained elusive. We demonstrate numerically that in sharp contrast to monolayer graphene, the normalized autocorrelation function for the puddle landscape in bilayer graphene depends only on the distance between the graphene and the source of the long-ranged impurity potential. By comparing with available experimental data, we find quantitative evidence for the implied differences in scanning tunneling microscopy measurements of electron and hole puddles for monolayer and bilayer graphene in nominally the same disorder potential.