Imaging the dynamics of free-electron Landau states

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 observatio...

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Main Authors:	Schattschneider, P., Schachinger, Th., Stöger-Pollach, M., Löffler, S., Steiger-Thirsfeld, A., Bliokh, K. Y., Nori, Franco
Format:	Online
Language:	English
Published:	Nature Pub. Group 2014
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4143940/

id	pubmed-4143940
recordtype	oai_dc
spelling	pubmed-41439402014-09-03 Imaging the dynamics of free-electron Landau states Schattschneider, P. Schachinger, Th. Stöger-Pollach, M. Löffler, S. Steiger-Thirsfeld, A. Bliokh, K. Y. Nori, Franco Article 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. Nature Pub. Group 2014-08-08 /pmc/articles/PMC4143940/ /pubmed/25105563 http://dx.doi.org/10.1038/ncomms5586 Text en Copyright © 2014, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved. http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Schattschneider, P. Schachinger, Th. Stöger-Pollach, M. Löffler, S. Steiger-Thirsfeld, A. Bliokh, K. Y. Nori, Franco
spellingShingle	Schattschneider, P. Schachinger, Th. Stöger-Pollach, M. Löffler, S. Steiger-Thirsfeld, A. Bliokh, K. Y. Nori, Franco Imaging the dynamics of free-electron Landau states
author_facet	Schattschneider, P. Schachinger, Th. Stöger-Pollach, M. Löffler, S. Steiger-Thirsfeld, A. Bliokh, K. Y. Nori, Franco
author_sort	Schattschneider, P.
title	Imaging the dynamics of free-electron Landau states
title_short	Imaging the dynamics of free-electron Landau states
title_full	Imaging the dynamics of free-electron Landau states
title_fullStr	Imaging the dynamics of free-electron Landau states
title_full_unstemmed	Imaging the dynamics of free-electron Landau states
title_sort	imaging the dynamics of free-electron landau states
description	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.
publisher	Nature Pub. Group
publishDate	2014
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4143940/
_version_	1613127515050606592

Imaging the dynamics of free-electron Landau states

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