Title
Electron vortex beams in a magnetic field : a new twist on Landau levels and Aharonov-Bohm states Electron vortex beams in a magnetic field : a new twist on Landau levels and Aharonov-Bohm states
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
College Park, Md :American Physical Society ,
Subject
Physics
Source (journal)
Physical review X / American Physical Society. - College Park, Md, 2011, currens
Volume/pages
2(2012) :4 , p. 1-15
ISSN
2160-3308
Article Reference
041011
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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 nondiffracting 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. Interestingly, the nonrotating superpositions reproduce stable multivortex configurations that appear in rotating superfluids. Our results open an avenue for the direct electron-microscopy observation of fundamental properties of free quantum-electron states in magnetic fields.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/98b9a5/2873.pdf
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