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  • Letter

General quantum-mechanical solution for twisted electrons in a uniform magnetic field

Liping Zou1,3,*, Pengming Zhang2,†, and Alexander J. Silenko3,4,5,‡

  • 1Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China
  • 2School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China
  • 3Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
  • 4Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
  • 5Research Institute for Nuclear Problems, Belarusian State University, Minsk 220030, Belarus

  • *zoulp@impcas.ac.cn
  • †Corresponding author: zhangpm5@mail.sysu.edu.cn
  • ‡alsilenko@mail.ru
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Phys. Rev. A 103, L010201 – Published 6 January, 2021

DOI: https://doi.org/10.1103/PhysRevA.103.L010201

Abstract

A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a specific case of unstructured electron waves. Unlike all precedent investigations, the present study describes structured electron states which are not plane waves along the magnetic field direction. In the weak-field limit, our solution (unlike the existing theory) is consistent with the well-known equation for free twisted electron beams. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted. Distinguishing features of the quantization of the velocity and the effective mass of the Laguerre-Gauss and Landau electrons in the uniform magnetic field are analyzed.

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Phys. Rev. A 103, L010201– Published 6 January, 2021
  • Received 9 May 2020
  • Accepted 10 December 2020
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