title: Imaging the dynamics of free-electron Landau states.
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.
authors.affiliation: 1] Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria [2] LMSSMat (CNRS UMR 8579) Ecole Centrale Paris, Châtenay-Malabry F-92295, France [3] University Service Centre for Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
authors.forename: P
authors.initials: P
authors.lastname: Schattschneider
authors.affiliation: Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
authors.forename: Th
authors.initials: T
authors.lastname: Schachinger
authors.affiliation: University Service Centre for Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
authors.forename: M
authors.initials: M
authors.lastname: Stöger-Pollach
authors.affiliation: University Service Centre for Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
authors.forename: S
authors.initials: S
authors.lastname: Löffler
authors.affiliation: University Service Centre for Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
authors.forename: A
authors.initials: A
authors.lastname: Steiger-Thirsfeld
authors.affiliation: 1] iTHES Research Group, RIKEN, Wako-shi, Saitama 351-0198, Japan [2] Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198, Japan.
authors.forename: K Y
authors.initials: KY
authors.lastname: Bliokh
authors.affiliation: 1] Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198, Japan [2] Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
authors.forename: Franco
authors.initials: F
authors.lastname: Nori
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