Thermal conductance of one-dimensional disordered harmonic chains

Biswarup Ash*, Ariel Amir, Yohai Bar-Sinai, Yuval Oreg, Yoseph Imry

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study heat conduction mediated by longitudinal phonons in one-dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that, suprisingly, the thermal conductance of a system with strong disorder, characterized by a "heavy-tailed" probability distribution, and with large impedance mismatch between the bath and the system, scales normally with the system size, i.e., in a manner consistent with Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

Original languageEnglish
Article number121403
JournalPhysical Review B
Volume101
Issue number12
DOIs
StatePublished - 15 Mar 2020
Externally publishedYes

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