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Anomalous phonon dispersion near yielding in athermal crystals

Fumiaki Nakai1,*, Michio Otsuki2, Kuniyasu Saitoh3, and Hiroaki Katsuragi1

  • 1Department of Earth and Space Science, The University of Osaka, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
  • 2Institute of Science and Engineering, Shimane University, 1060 Nishikawatsu-cho, Matsue, Shimane 690-8504, Japan
  • 3Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan

  • *Contact author: fumiaki.nakai@ess.sci.osaka-u.ac.jp
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Phys. Rev. E 114, 025422 – Published 26 August, 2026

DOI: https://doi.org/10.1103/3lnj-1ml1

Abstract

Vibrational properties of ordered athermal solids near yielding remain poorly understood. We show that yielding in a sheared crystal is governed not by a single localized instability but by directionally extended multimode softening that forms a cross-shaped low-frequency region in wave number space. Near yielding, the acoustic dispersion ω∼k is replaced by ω∼k2 along the soft direction, and the vibrational density of states crosses over from Debye to non-Debye scaling, with a diverging length scale. We analytically derive these scaling laws.

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Phys. Rev. E 114, 025422– Published 26 August, 2026
  • Received 31 March 2026
  • Accepted 15 July 2026
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