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Anyons in a weakly interacting system

Nature Physics volume 3, pages 796–801 (2007)Cite this article

Abstract

In quantum theory, indistinguishable particles in three-dimensional space behave in only two distinct ways. On interchange, their wavefunction maps either to itself if the particles are bosons, or to minus itself if they are fermions. In two dimensions, a more exotic possibility arises: on exchange of two particles known as anyons, the wavefunction acquires the phase . Such fractional exchange statistics are normally regarded as the hallmark of strong correlations. Here, we describe a theoretical proposal for a system whose excitations are anyons with the exchange phase θ=π/4 and charge ±e/2, but at the same time can be built by filling a set of single-particle states of essentially non-interacting electrons. The system consists of an artificially structured type-II superconducting film adjacent to a two-dimensional electron gas in the integer quantum Hall regime with unit filling fraction. The proposed set-up enables manipulation of these anyons and could prove useful in schemes for fault-tolerant topological quantum computation.

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Figure 1: Schematic diagram of the proposed device.
Figure 2: Properties of the continuum model.
Figure 3: Properties of the lattice model.

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Acknowledgements

The authors are indebted to M. Berciu and A. Vishwanath for some key suggestions and wish to thank I. Affleck, D. Fisher, D. Haldane, C. Kallin, A. Kitaev, K. Shtengel, D. Scalapino and Z. Tesanovic for stimulating discussions and correspondence. The work reported here was supported by NSERC, CIAR and the Killam Foundation.

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  1. Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada

    C. Weeks, G. Rosenberg, B. Seradjeh & M. Franz

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  1. C. Weeks
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Correspondence to M. Franz.

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Weeks, C., Rosenberg, G., Seradjeh, B. et al. Anyons in a weakly interacting system. Nature Phys 3, 796–801 (2007). https://doi.org/10.1038/nphys730

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