A lower bound to the thermal diffusivity of insulators

Abstract

It has been known for decades that thermal conductivity of insulating crystals becomes proportional to the inverse of temperature when the latter is comparable to or higher than the Debye temperature. This behavior has been understood as resulting from Umklapp scattering among phonons. We put under scrutiny the magnitude of the thermal diffusion constant in this regime and find that it does not fall below a threshold set by the square of sound velocity times the Planckian time (${\tau }_p=\hslash /k_{B}T$). The conclusion, based on scrutinizing the ratio in cubic crystals with high thermal resistivity, appears to hold even in glasses where Umklapp events are not conceivable. Explaining this boundary, reminiscent of a recently-noticed limit for charge transport in metals, is a challenge to theory.

7 pages, 3 figures

References in corpus (5)

• Theory of universal incoherent metallic transport
• Quantum chaos on a critical Fermi surface
• Ab Initio Phonon Dispersions for PbTe
• Anharmonic phonon spectra of PbTe and SnTe in the self-consistent harmonic approximation
• Finding merit in dividing neighbors

Cited by in corpus (5)

• Universal Bounds on Transport in Holographic Systems with Broken Translations
• Thermalization and Possible Signatures of Quantum Chaos in Complex Crystalline Materials
• Phonon hydrodynamics in crystalline GeTe at low temperature
• Strongly coupled quantum phonon fluid in a solvable model
• A spatially resolved optical method to measure thermal diffusivity