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Two-dimensional Anderson localization and KPZ subuniversality classes: Sensitivity to boundary conditions and insensitivity to symmetry classes

Nyayabanta Swain1,2,*, Shaffique Adam3,4, and Gabriel Lemarié1,2,5,6,†

  • *Contact author: nyayabanta@gmail.com
  • †Contact author: gabriel.lemarie@cnrs.fr
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Phys. Rev. Research 8, 013038 – Published 15 January, 2026

DOI: https://doi.org/10.1103/pbrz-3lrl

Abstract

We challenge two foundational principles of localization physics by analyzing conductance fluctuations in two dimensions with unprecedented precision: (1) the Thouless criterion, which defines localization as insensitivity to boundary conditions, and (2) that symmetry determines the universality class of Anderson localization. We reveal that the fluctuations of the conductance logarithm fall into distinct subuniversality classes inherited from Kardar-Parisi-Zhang (KPZ) physics, dictated by the lead configurations of the scattering system and unaffected by the presence of a magnetic field. Distinguishing between these probability distributions poses a significant challenge due to their striking similarity, requiring sampling beyond the usual threshold of ∼10−6 accessible through independent disorder realizations. To overcome this, we implement an importance sampling scheme—a Monte Carlo approach in disorder space—that enables us to probe rare disorder configurations and sample probability distribution tails down to 10−30. This unprecedented precision allows us to unambiguously differentiate between KPZ subuniversality classes of conductance fluctuations for different lead configurations, while demonstrating the insensitivity to magnetic fields.

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Phys. Rev. Research 8, 013038– Published 15 January, 2026
  • Received 8 May 2025
  • Accepted 3 December 2025
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