On the Planckian bound for heat diffusion in insulators

Abstract

High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime $\tau \gtrsim {\tau }_{\text{Pl}}\equiv \hslash /(k_{B}T)$, despite phonon dynamics being entirely classical at these temperatures. 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, $\tau /{\tau }_{\text{Pl}}\approx v_M/v_s$ at high temperatures. The velocity bound therefore implies the Planckian bound.

10 pages + refs and appendices. 2 figures. v2: improved derivation of the velocity bound