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arXiv · 1204.2780

Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states

Konstantin Y. Bliokh·Peter Schattschneider·Jo Verbeeck·Franco Nori
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Abstract

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.

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Konstantin Y. Bliokh, Peter Schattschneider, Jo Verbeeck, Franco Nori. 2012-10-02. Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states. https://doi.org/10.1103/physrevx.2.041011

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