On the Planckian bound for heat diffusion in insulators


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 ∕ (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, ττPlvMvs at high temperatures. The velocity bound therefore implies the Planckian bound.

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Fig. 1: Melting velocity versus mechanical (sound) velocity for various classes of non-metallic compound.
Fig. 2: Ratio of timescales ττPl versus the ratio of velocities vMvs.
Fig. 3: τPlτ × vMvs against δ2.

Data availability

The data represented in Figs. 13 are available as Source Data 13. All other data that support the plots within this paper and other findings of this study are given in the Supplementary Information and are furthermore available from the corresponding author upon reasonable request.


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We thank K. Behnia, A. Kapitulnik, S. Kivelson and J. Zaanen for their insightful comments and criticism. We also thank Z. Han and D. Shi for discussions on related topics. This work is supported by the Department of Energy, Office of Basic Energy Sciences, under contract no. DEAC02-76SF00515. C.H.M. is supported by an NSF graduate fellowship.

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C.H.M. and S.A.H. both conceived and performed the research, and wrote the paper.

Correspondence to Sean A. Hartnoll.

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Supplementary Information

Supplementary table and refs. 1–45.

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Source Data Fig. 1

Labelled data points.

Source Data Fig. 2

Labelled data points.

Source Data Fig. 3

Labelled data points.

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Mousatov, C.H., Hartnoll, S.A. On the Planckian bound for heat diffusion in insulators. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0828-6

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