On the Planckian bound for heat diffusion in insulators

2019/08/31 by Connie H. Mousatov, Sean A. Hartnoll · 39 citations
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Bound state #Diffusion #Insulator (electricity) #Phonon #Quantum and electron transport phenomena #Second sound #Thermal #Thermal diffusivity #Thermal properties of materials #Upper and lower bounds #cond-mat.mtrl-sci #cond-mat.stat-mech

paper · pdf · doi:10.1038/s41567-020-0828-6

published in Nature Physics 16(5), 579-584 (Nature Portfolio) · 10 pages + refs and appendices. 2 figures. v2: improved derivation of the velocity bound

openalex created_date 2019/08/22 · arxiv created 2019/09/11 · openalex publication_date 2020/03/16 · arxiv updated 2020/06/24 · openalex updated_date 2026/08/05

Abstract

High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime τ\gtrsim τ_Pl ≡ ℏ/(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, τ/τ_Pl ≈ v_M/v_s at high temperatures. The velocity bound therefore implies the Planckian bound.

Citations

• Nonmetallic crystals with high thermal conductivity
• Interpretation of the Thermal Conductivity of Glasses
• Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation