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Title: 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 ≳ τPl ≡ ℏ / (kBT). Here, we argue that this Planckian bound is due to a quantum-mechanical bound on the sound velocity: vs < vM. The ‘melting velocity’ vM 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 / τPl ≈ vM / vs at high temperatures. The velocity bound therefore implies the Planckian bound.

Authors:
 [1]; ORCiD logo [2]
  1. Stanford Univ., CA (United States)
  2. Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1608310
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Nature Physics
Additional Journal Information:
Journal Volume: 16; Journal Issue: 5; Journal ID: ISSN 1745-2473
Publisher:
Nature Publishing Group (NPG)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Mousatov, Connie H., and Hartnoll, Sean A. On the Planckian bound for heat diffusion in insulators. United States: N. p., 2020. Web. doi:10.1038/s41567-020-0828-6.
Mousatov, Connie H., & Hartnoll, Sean A. On the Planckian bound for heat diffusion in insulators. United States. doi:https://doi.org/10.1038/s41567-020-0828-6
Mousatov, Connie H., and Hartnoll, Sean A. Mon . "On the Planckian bound for heat diffusion in insulators". United States. doi:https://doi.org/10.1038/s41567-020-0828-6. https://www.osti.gov/servlets/purl/1608310.
@article{osti_1608310,
title = {On the Planckian bound for heat diffusion in insulators},
author = {Mousatov, Connie H. and Hartnoll, Sean A.},
abstractNote = {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 ≳ τPl ≡ ℏ / (kBT). Here, we argue that this Planckian bound is due to a quantum-mechanical bound on the sound velocity: vs < vM. The ‘melting velocity’ vM 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 / τPl ≈ vM / vs at high temperatures. The velocity bound therefore implies the Planckian bound.},
doi = {10.1038/s41567-020-0828-6},
journal = {Nature Physics},
number = 5,
volume = 16,
place = {United States},
year = {2020},
month = {3}
}

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