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Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

Nature Physics volume 3, pages 561–565 (2007)Cite this article

Abstract

Recent theories suggest that the quasiparticles that populate certain quantum Hall states should exhibit exotic braiding statistics that could be used to build topological quantum gates. Confined systems that support such states at a filling fraction ν=5/2 are of particular interest for testing these predictions. Here, we report transport measurements of just such a system, which consists of a quantum point contact (QPC) in a two-dimensional GaAs/AlGaAs electron gas that itself exhibits a well-developed fractional quantum Hall effect at a bulk filling fraction νbulk=5/2. We observe plateau-like features at an effective filling fraction of νQPC=5/2 for lithographic contact widths of 1.2 μm and 0.8 μm, but not 0.5 μm. Transport near νQPC=5/2 in the QPCs is consistent with a picture of chiral Luttinger-liquid edge states with inter-edge tunnelling, suggesting that an incompressible state at νQPC=5/2 forms in this confined geometry.

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Figure 1: Device and measurement set-up.
Figure 2: Bulk transport measurements, including T dependence.
Figure 3: Action of the QPC, compared with concurrent bulk measurements.
Figure 4: Observation of structure near quantized values in various QPCs.
Figure 5: Temperature dependence of the 5/2 state in the 1.2 μm QPC.
Figure 6: Dependence on d.c. current bias of the 5/2 and 7/3 states in the 1.2 μm QPC.

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Acknowledgements

We gratefully acknowledge helpful discussions with M. Fisher, B. Halperin, A. Johnson, E.-A. Kim, B. Rosenow, A. Stern, X.-G. Wen and A. Yacoby. This research was supported in part by the Microsoft Corporation Project Q, HCRP at Harvard University, ARO (W911NF-05-1-0062), the NSEC program of the NSF (PHY-0117795) and NSF (DMR-0353209) at MIT.

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Authors and Affiliations

  1. Division of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA

    Jeffrey B. Miller

  2. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Iuliana P. Radu, Dominik M. Zumbühl & Marc A. Kastner

  3. Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

    Dominik M. Zumbühl

  4. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Eli M. Levenson-Falk & Charles M. Marcus

  5. Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, USA

    Loren N. Pfeiffer & Ken W. West

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Correspondence to Charles M. Marcus.

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Miller, J., Radu, I., Zumbühl, D. et al. Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2. Nature Phys 3, 561–565 (2007). https://doi.org/10.1038/nphys658

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