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Phonon hydrodynamic regimes in sapphire

Takuya Kawabata1, Kosuke Shimura1, Yuto Ishii1, Minatsu Koike1, Kentaro Yoshida1, Shu Yonehara1, Kohei Yokoi1, Alaska Subedi2, Kamran Behnia3,* et al.

Yo Machida1,†

  • *Contact author: kamran.behnia@espci.fr
  • †Contact author: yo.machida@gakushuin.ac.jp
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Phys. Rev. Research 7, 033017 – Published 7 July, 2025

DOI: https://doi.org/10.1103/ptds-chrz

Abstract

When an ideal insulator is cooled, four regimes of thermal conductivity are expected to emerge one after another. Two of these, the Ziman and the Poiseuille, are hydrodynamic regimes in which collision among phonons are mostly normal. It has been difficult to observe them, save for a few insulators with high levels of isotopic and chemical purity. Our thermal transport measurements, covering four decades of temperatures between 0.1 K and 900 K, reveal that sapphire displays all four regimes, despite its isotopic impurity. In the Ziman regime, the thermal conductivity exponentially increases, attaining an amplitude as large as 35 000 W/Km. We show that the peak thermal conductivity of ultrapure, simple insulators, including diamond, silicon, and solid helium, is set by a universal scaling depending on isotopic purity. The thermal conductivity of sapphire is an order of magnitude higher than what is expected by this scaling. We argue that this may be caused by the proximity of optical and acoustic phonon modes, as a consequence of the large number of atoms in the primitive cell.

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Phys. Rev. Research 7, 033017– Published 7 July, 2025
  • Received 23 July 2024
  • Accepted 16 June 2025
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