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The nature of localization in graphene under quantum Hall conditions


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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Figure 1: The Landau-level spectrum in monolayer graphene extracted from compressibility measurements.
Figure 2: Measured spectrum of localized states in graphene.
Figure 3: Single-particle picture of localization in a perpendicular magnetic field.
Figure 4: The dependence of the measured electrostatic potential on the compressibility of graphene.
Figure 5: The behaviour of localized states in the presence of nonlinear screening due to Coulomb repulsion.
Figure 6: The magnetic-field dependence of the width in density of the incompressible region.


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We would like to acknowledge useful discussions with Y. Meir and A. Auerbach. This work is partly supported by the Harvard NSEC.

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Authors and Affiliations



J.M.: designing the experiment, sample preparation, measurements, data analysis, preparation of the manuscript. N.A.: measurements, data analysis. G.U.: sample preparation. T.L.: sample preparation. K.v.K.: preparation of the manuscript. J.H.S.: designing the experiment, data analysis, preparation of the manuscript. A.Y.: designing the experiment, data analysis, preparation of the manuscript.

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Correspondence to A. Yacoby.

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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).

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