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Local charge of the ν = 5/2 fractional quantum Hall state

Nature volume 469, pages 185–188 (2011)Cite this article

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Abstract

Electrons moving in two dimensions under the influence of strong magnetic fields effectively lose their kinetic energy and display exotic behaviour dominated by Coulomb forces. When the ratio of electrons to magnetic flux quanta in the system (ν) is near 5/2, the electrons are predicted to condense into a correlated phase with fractionally charged quasiparticles and a ground-state degeneracy that grows exponentially as these quasiparticles are introduced1. The only way for electrons to transform between the many ground states would be to braid the fractional excitations around each other. This property has been proposed as the basis of a fault-tolerant quantum computer2. Here we present observations of localized quasiparticles at ν = 5/2, confined to puddles by disorder. Using a local electrometer to compare how quasiparticles at ν = 5/2 and ν = 7/3 charge these puddles, we were able to extract the ratio of local charges for these states. Averaged over several disorder configurations and samples, we found the ratio to be 4/3, suggesting that the local charges are = e/3 and = e/4, where e is the charge of an electron. This is in agreement with theoretical predictions for a paired state at ν = 5/2. Confirming the existence of localized e/4 quasiparticles shows that proposed interferometry experiments to test statistics and computational ability of the state at ν = 5/2 would be possible.

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Figure 1: Filling puddles with fractional charge.
Figure 2: Incompressibility and localized states at 5/2.
Figure 3: Comparison of spectra at 5/2 and 7/3.
Figure 4: Summary of data and model.

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Acknowledgements

We would like to acknowledge B. Verdene, J. Waissman and J. Nübler for technical assistance, and B. Halperin for theoretical discussions. We acknowledge financial support from Microsoft Corporation Project Q and the National Science Foundation’s Graduate Research Fellowship Program.

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Authors and Affiliations

  1. Department of Physics, Harvard University, 11 Oxford Street, Cambridge, Massachusetts 02138, USA,

    Vivek Venkatachalam & Amir Yacoby

  2. Department of Electrical Engineering, Princeton University, Princeton, 08544, New Jersey, USA

    Loren Pfeiffer & Ken West

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  1. Vivek Venkatachalam
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  2. Amir Yacoby
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Contributions

V.V. conceived and designed the experiments, prepared samples, carried out the experiments and data analysis, and wrote the paper. A.Y. conceived and designed the experiments, carried out data analysis and wrote the paper. L.P. and K.W. carried out the molecular beam epitaxy growth.

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Correspondence to Amir Yacoby.

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The authors declare no competing financial interests.

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Supplementary Information

The file contains Supplementary text on the correlation extraction procedure, an additional reference and Supplementary Figures 1-4 with legends. (PDF 254 kb)

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Venkatachalam, V., Yacoby, A., Pfeiffer, L. et al. Local charge of the ν = 5/2 fractional quantum Hall state. Nature 469, 185–188 (2011). https://doi.org/10.1038/nature09680

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