Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor

TL;DR

This study visualizes electron-hole puddles in graphene near the neutrality point using a scanning single electron transistor, confirming theoretical predictions and providing local density of states measurements.

Contribution

First direct imaging of electron-hole puddles in graphene near the neutrality point using a scanning single electron transistor.

Findings

Electron-hole puddles are observed as predicted theoretically.

The local density of states matches the kinetic contribution, indicating weak exchange and correlation effects.

The measurement technique allows local density of states determination in graphene.

Abstract

The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.