On the Planckian bound for heat diffusion in insulators

Abstract

In an insulator, thermal transport at high temperature is expected to be dominated by entirely classical phonon dynamics. In apparent tension with this expectation, recent experimental observations have led to the conjecture that the transport lifetime, τ, is subject to a Planckian bound from below, namely, τ ≳ τ Pl ≡ ℏ / (k B T). Here, we argue that this Planckian bound is due to a quantum-mechanical bound on the sound velocity: v s < v M . The ‘melting velocity’ v M is defined in terms of the melting temperature of the crystal, the interatomic spacing and Planck’s constant. We show that for several classes of insulating crystals, both simple and complex, τ / τ Pl ≈ v M / v s at high temperatures. The velocity bound therefore implies the Planckian bound.