Particle localization is an essential ingredient in quantum Hall physics. In conventional high-mobility two-dimensional electron systems such as in GaAs/AlGaAs semiconductor heterostructures, Coulomb interactions were shown to compete with disorder and to have a central role in particle localization. Here, we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller than in GaAs two-dimensional electron systems. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single-electron transistor. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single-particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.
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Martin, J., Akerman, N., Ulbricht, G. et al. The nature of localization in graphene under quantum Hall conditions. Nature Phys 5, 669–674 (2009). https://doi.org/10.1038/nphys1344
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