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Spatially resolved edge currents and guided-wave electronic states in graphene

Nature Physics volume 12, pages 128–133 (2016)Cite this article

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Abstract

Exploiting the light-like properties of carriers in graphene could allow extreme non-classical forms of electronic transport to be realized1,2,3,4,5,6,7,8. In this vein, finding ways to confine and direct electronic waves through nanoscale streams and streamlets, unimpeded by the presence of other carriers, has remained a grand challenge9,10,11,12. Inspired by guiding of light in fibre optics, here we demonstrate a route to engineer such a flow of electrons using a technique for mapping currents at submicron scales. We employ real-space imaging of current flow in graphene to provide direct evidence of the confinement of electron waves at the edges of a graphene crystal near charge neutrality. This is achieved by using superconducting interferometry in a graphene Josephson junction and reconstructing the spatial structure of conducting pathways using Fourier methods13. The observed edge currents arise from coherent guided-wave states, confined to the edge by band bending and transmitted as plane waves. As an electronic analogue of photon guiding in optical fibres, the observed states afford non-classical means for information transduction and processing at the nanoscale.

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Figure 1: ‘Fibre-optic’ modes and spatially resolved current imaging in a graphene Josephson junction.
Figure 2: Gate-tunable evolution of edge and bulk current-carrying states in monolayer graphene.
Figure 3: Edge and bulk currents in bilayer graphene with and without transverse electric field.
Figure 4: ‘Fibre-optic’ theoretical model of transport in graphene.

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Acknowledgements

The authors thank O. Dial, B. Halperin, V. Manucharyan and J. Sau for helpful discussions. This work is supported by the Center for Integrated Quantum Materials (CIQM) under NSF award 1231319 (L.S.L. and O.S.) and the US DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award DE-SC0001819 (P.J.-H., M.T.A., A.Y.). Nanofabrication was performed at the Harvard Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network (NNIN) supported by NSF award ECS-0335765. A.R.A. was supported by the Foundation for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO/OCW). I.C.F. was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Project MUNATOP, the US–Israel Binational Science Foundation, and the Minerva Foundation.

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Authors and Affiliations

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

    M. T. Allen & A. Yacoby

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

    O. Shtanko, P. Jarillo-Herrero & L. S. Levitov

  3. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

    I. C. Fulga

  4. Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1 2628 CJ Delft, The Netherlands,

    A. R. Akhmerov

  5. Environment and Energy Materials Division, National Institute for Materials Science, 1-1 Namiki, Tsukuba Ibaraki 305-0044, Japan,

    K. Watanabe & T. Taniguchi

Authors
  1. M. T. Allen
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Contributions

M.T.A. and A.Y. designed and fabricated the devices, performed the experiments, analysed the data, and wrote the paper. O.S. and L.S.L. developed the theoretical model of guided edge modes and wrote the paper. A.R.A. and I.C.F. performed the Bayesian analysis of the Fraunhofer patterns. P.J.-H. contributed to discussions of the results and wrote the paper. K.W. and T.T. provided the hexagonal boron nitride crystals used in device fabrication.

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Correspondence to A. Yacoby.

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The authors declare no competing financial interests.

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Allen, M., Shtanko, O., Fulga, I. et al. Spatially resolved edge currents and guided-wave electronic states in graphene. Nature Phys 12, 128–133 (2016). https://doi.org/10.1038/nphys3534

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