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Real-Space Imaging of Thomson Charge Configurations in Superfluid Helium Nanodroplets

Thomas Pohl1, Jan Mayerhofer1, Hanqing Liu2, Arin Mizouri3, Hao Sha2, Masoomeh Mahmoodi Darian1, Fabio Zappa1, Andrew M. Ellis2, David J. Wales4 et al.

Shengfu Yang2,* and Paul Scheier1,†

  • *Contact author: sfy1@leicester.ac.uk
  • †Contact author: paul.scheier@uibk.ac.at
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Phys. Rev. Lett. 137, 183001 – Published 26 October, 2026

DOI: https://doi.org/10.1103/qby4-bm6q

Abstract

Predicting the lowest-energy arrangement of like charges on a sphere defines the Thomson problem, a long-standing challenge with analytical solutions only for a few small systems. We report a real-space experimental realization using superfluid helium nanodroplets, where surface-localized charges are tagged by singly charged gold nanoparticles and recorded as transmission electron microscopy imprints. The observed configurations reveal Thomson charge ordering from finite-N minima to curvature-frustrated Coulomb crystallization, establishing helium nanodroplets as a directly imageable platform for charge organization on spherical surfaces.

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Phys. Rev. Lett. 137, 183001– Published 26 October, 2026
  • Received 15 June 2026
  • Revised 27 August 2026
  • Accepted 22 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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