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Imaging the dynamics of free-electron Landau states

Author

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  • P. Schattschneider

    (Institute of Solid State Physics, Vienna University of Technology
    LMSSMat (CNRS UMR 8579) Ecole Centrale Paris
    University Service Centre for Electron Microscopy, Vienna University of Technology)

  • Th. Schachinger

    (Institute of Solid State Physics, Vienna University of Technology)

  • M. Stöger-Pollach

    (University Service Centre for Electron Microscopy, Vienna University of Technology)

  • S. Löffler

    (University Service Centre for Electron Microscopy, Vienna University of Technology)

  • A. Steiger-Thirsfeld

    (University Service Centre for Electron Microscopy, Vienna University of Technology)

  • K. Y. Bliokh

    (iTHES Research Group, RIKEN
    Center for Emergent Matter Science, RIKEN)

  • Franco Nori

    (Center for Emergent Matter Science, RIKEN
    University of Michigan)

Abstract

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.

Suggested Citation

  • P. Schattschneider & Th. Schachinger & M. Stöger-Pollach & S. Löffler & A. Steiger-Thirsfeld & K. Y. Bliokh & Franco Nori, 2014. "Imaging the dynamics of free-electron Landau states," Nature Communications, Nature, vol. 5(1), pages 1-6, December.
    • Handle: RePEc:nat:natcom:v:5:y:2014:i:1:d:10.1038_ncomms5586
    DOI: 10.1038/ncomms5586
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