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# Observation of electron–hole puddles in graphene using a scanning single-electron transistor

## Abstract

The electronic structure of graphene causes its charge carriers to behave like relativistic particles. For a perfect graphene sheet free from impurities and disorder, the Fermi energy lies at the so-called ‘Dirac point’, where the density of electronic states vanishes. But in the inevitable presence of disorder, theory predicts that equally probable regions of electron-rich and hole-rich puddles will arise. These puddles could explain graphene’s anomalous non-zero minimal conductivity at zero average carrier density. Here, we use a scanning single-electron transistor to map the local density of states and the carrier density landscape in the vicinity of the neutrality point. Our results confirm the existence of electron–hole puddles, and rule out extrinsic substrate effects as explanations for their emergence and topology. Moreover, we find that, unlike non-relativistic particles the density of states can be quantitatively accounted for by considering non-interacting electrons and holes.

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## Acknowledgements

We acknowledge helpful discussions on the preparation of graphene flakes with K. Novoselov and A. Geim. We would also like to acknowledge fruitful discussions with F. von Oppen.

## Author information

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Correspondence to A. Yacoby.

## Supplementary information

### Supplementary Information

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Martin, J., Akerman, N., Ulbricht, G. et al. Observation of electron–hole puddles in graphene using a scanning single-electron transistor. Nature Phys 4, 144–148 (2008). https://doi.org/10.1038/nphys781

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• DOI: https://doi.org/10.1038/nphys781

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