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Imaging the transition from diffusive to Landauer resistivity dipoles

Serhii Kovalchuk1,2,3, David Kämpfer1,2,4, Jonathan K. Hofmann1,2,4, Timofey Balashov1,2,5, Vasily Cherepanov1,2, Bert Voigtländer1,2,4, Ireneusz Morawski3, F. Stefan Tautz1,2,4, and Felix Lüpke1,2,6,*

  • *Contact author: f.luepke@fz-juelich.de
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Phys. Rev. B 114, 165411 – Published 11 September, 2026

DOI: https://doi.org/10.1103/psjh-gjh8

Abstract

A pointlike defect in a uniform current-carrying conductor induces a dipole in the electrochemical potential, which counteracts the original transport field. If the mean free path of the carriers is much smaller than the size of the defect, then the dipole results from the purely diffusive motion of the carriers around the defect. In the opposite limit, ballistic carriers scatter from the defect—for this situation, Landauer postulated the emergence of residual resistivity dipoles that are independent of the defect size and thus impose a fundamental limit on the resistance of the parent conductor. Here, we study resistivity dipoles around holes of different sizes in two-dimensional Bi films on Si(111). Using scanning tunneling potentiometry to image the dipoles, we find a crossover from linear to constant scaling behavior of their amplitudes with defect size, manifesting the transition from diffusive to Landauer dipoles. The extracted parameters of the transition allow us to estimate the Fermi wave vector and the carrier mean free path in our Bi films.

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Phys. Rev. B 114, 165411– Published 11 September, 2026
  • Received 17 January 2025
  • Revised 7 July 2026
  • Accepted 9 July 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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