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Imaging magnetic focusing of coherent electron waves

Nature Physics volume 3, pages 464–468 (2007)Cite this article

Abstract

The coherent flow of electrons through a two-dimensional electron gas1,2,3,4,5,6,7,8 (2DEG) offers promising approaches for spintronics8,9,10 and quantum information processing11,12. Cryogenic scanning probe microscopes (SPMs) are a valuable tool for imaging electron motion13,14,15,16,17,18,19,20,21,22,23,24,25, but have been limited by their inability to follow such motion through an open structure under an applied magnetic field. Here we report a way to visualize the flow of electron waves from one point to another by using the SPM tip to create a lens in the 2DEG below. The lens deflects electrons and casts a shadow downstream. We use this technique to image magnetic focusing in a GaAs 2DEG. Magnetic focusing occurs when electrons flowing from one quantum point contact (QPC) rejoin at a second QPC a number of cyclotron diameters away3,4,9,26,27. Our images show semicircular trajectories as the electrons bounce along the boundary, as well as fringes created by the interference of multiple paths, demonstrating that the flow is coherent18,19,28. Remarkable agreement between experiment and theory demonstrates our ability to visualize electron trajectories in a magnetic field, and to make a new type of imaging electron interferometer.

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Figure 1: Set-up for SPM images and simulations of magnetic focusing in a 2DEG.
Figure 2: Experimental SPM images of magnetic focusing in a 2DEG at 4.2 K recorded near the first three magnetic focusing peaks.
Figure 3: Quantum simulations of SPM images including small-angle scattering.
Figure 4: Direct comparison of interference fringes between experiment and theory for different tip strengths.

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Acknowledgements

This work has been performed with support at Harvard University from the ARO, the NSF-funded Nanoscale Science and Engineering Center (NSEC), and the DFG (Emmy-Noether program). Work at Santa Barbara has been supported in part by the Institute for Quantum Engineering, Science and Technology (iQUEST). We would also like to thank the National Nanotechnology Infrastructure Network (NNIN) and the Harvard CrimsonGrid for computing resources.

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Author notes

  1. Katherine E. Aidala

    Present address: Present address: Dept. of Physics, Mount Holyoke College, South Hadley, Massachusetts 01075, USA,

Authors and Affiliations

  1. Div. of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

    Katherine E. Aidala & R. M. Westervelt

  2. Dept. of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Robert E. Parrott, Tobias Kramer, E. J. Heller & R. M. Westervelt

  3. Dept. of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

    E. J. Heller

  4. Dept. of Materials Science, University of California, Santa Barbara, California 93106, USA

    M. P. Hanson & A. C. Gossard

Authors
  1. Katherine E. Aidala
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  4. E. J. Heller
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Contributions

K.E.A. conducted the experiments with R.M.W.; R.E.P. and T.K. carried out classical and quantum simulations of electron flow with E.J.H. and M.P.H. grew the semiconductor heterostructure with A.C.G.

Corresponding authors

Correspondence to Katherine E. Aidala or R. M. Westervelt.

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The authors declare no competing financial interests.

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Aidala, K., Parrott, R., Kramer, T. et al. Imaging magnetic focusing of coherent electron waves. Nature Phys 3, 464–468 (2007). https://doi.org/10.1038/nphys628

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