Phonon hydrodynamic regimes in sapphire

TL;DR

This study demonstrates that sapphire exhibits all four phonon hydrodynamic regimes across a wide temperature range, revealing insights into thermal conductivity behavior in insulators with implications for understanding phonon transport.

Contribution

The paper provides the first comprehensive experimental observation of all four phonon hydrodynamic regimes in sapphire, including the Ziman and Poiseuille regimes, despite its impurity levels.

Findings

Sapphire shows all four phonon regimes over four decades of temperature.

Thermal conductivity peaks at 35,000 W/Km in the Ziman regime.

Sapphire's thermal conductivity exceeds universal scaling predictions, likely due to optical-acoustic phonon mode proximity.

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 ultra-pure, simple insulators, including diamond, silicon and solid helium, is set by a universal scaling depending on isotropic 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.