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Remarkable heat conduction mediated by non-equilibrium phonon polaritons

Nature volume 623, pages 307–312 (2023)Cite this article

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Abstract

Surface waves can lead to intriguing transport phenomena. In particular, surface phonon polaritons (SPhPs), which result from coupling between infrared light and optical phonons, have been predicted to contribute to heat conduction along polar thin films and nanowires1. However, experimental efforts so far suggest only very limited SPhP contributions2,3,4,5. Through systematic measurements of thermal transport along the same 3C-SiC nanowires with and without a gold coating on the end(s) that serves to launch SPhPs, here we show that thermally excited SPhPs can substantially enhance the thermal conductivity of the uncoated portion of these wires. The extracted pre-decay SPhP thermal conductance is more than two orders of magnitude higher than the Landauer limit predicted on the basis of equilibrium Bose–Einstein distributions. We attribute the notable SPhP conductance to the efficient launching of non-equilibrium SPhPs from the gold-coated portion into the uncoated SiC nanowires, which is strongly supported by the observation that the SPhP-mediated thermal conductivity is proportional to the length of the gold coating(s). The reported discoveries open the door for modulating energy transport in solids by introducing SPhPs, which can effectively counteract the classical size effect in many technologically important films and improve the design of solid-state devices.

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Fig. 1: SiC nanowire sample and measurement scheme.
Fig. 2: Measured thermal properties of Sample S1.
Fig. 3: The thermal conductance of SPhPs induced by Au coating for Sample S1.
Fig. 4: Correlation between the nanowire structure, SPhP propagation and thermal properties.

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Data availability

Source data for the main figures are provided with this paper. Source data are provided with this paper.

Code availability

Original MATLAB codes used to solve for the dispersions and attenuations of bulk (Source code 1) and SPhPs (Source code 2) in Extended Data Fig. 1 are provided with this paper.

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Acknowledgements

We thank A. Majumdar, G. Chen, P. Reddy, G. Walker, J. Valentine, S. Shen, L. Yang and P. Gao for helpful discussions. Z.P. and D.L. thank the financial support from the National Science Foundation (award nos. 1903645 and 2114278). G.L. acknowledges support from the Army Research Office under grants W911NF-21-1-0119 and W911NF-22-P-0029. J.D.C. would like to acknowledge support from the Office of Naval Research under grant N00014-22-1-2035. Density-functional-theory-based calculations (L.L., X.L. and R.J.) were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Computational resources were provided by the Compute and Data Environment for Science (CADES) at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC05-00OR22725, and by the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC02-05CH11231.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Vanderbilt University, Nashville, TN, USA

    Zhiliang Pan, Guanyu Lu, Joshua D. Caldwell & Deyu Li

  2. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Xun Li, Rinkle Juneja & Lucas Lindsay

  3. Vanderbilt Institute of Nanoscale Science and Engineering, Vanderbilt University, Nashville, TN, USA

    James R. McBride

  4. Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, TN, USA

    Mackey Long

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Contributions

D.L. and Z.P. designed the thermal experiment and analysed the data. Z.P. conducted the thermal measurements and SEM characterizations. G.L. and J.D.C. performed s-SNOM measurements and CST modelling, with assistance from M.L. X.L., R.J. and L.L. performed first-principles calculations on optical phonon scattering and equilibrium thermal conductance. Z.P. and J.R.M. conducted the TEM examination. D.L., J.D.C. and L.L. directed the thermal experiments, optical experiments and theoretical calculations, respectively. D.L. and Z.P. drafted the manuscript, with input from all authors. All authors participated in the writing and discussions.

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Correspondence to Deyu Li.

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Extended data figures and tables

Extended Data Fig. 1 Theoretical calculations.

Calculated SiC SPhP dispersions (a,b) and attenuations for different radii and branches (c,d). Note that all higher-order modes (n > 1) overlap with the first-order mode (n = 1) in the upper two panels, showing the SPhP dispersion. The sloped dashed and solid lines indicate the SiC and the free-space light lines in the upper two panels, respectively.

Extended Data Fig. 2 Further experimental data.

a, The overlapping thermal conductivity of an uncoated SiC nanowire measured with two different suspended lengths, indicating negligible contact thermal resistance. b, Extracted SPhP thermal conductivity (brown symbols) and percentage enhancement (blue symbols). Inset shows the sample bridging the two membranes, with the Au-coated segment placed on one membrane. c, An SEM micrograph of the sample after most of the suspended bare SiC nanowire was cut off by a sharp probe. d, Thermal conductance between membranes for the device with the Au-coated segment as shown in c (brown symbols) and a blank device of identical dimension (black symbols).

Supplementary information

Supplementary Information

This file contains further theoretical simulation information, sample preparation details for thermal measurements, uncertainty analysis, thermal data summary, further optical results, Supplementary Figs. 1–22, Supplementary Tables 1 and 2 and Supplementary References.

Peer Review File

Source Code 1

Original MATLAB code used to solve for the dispersions and attenuations of bulk in Extended Data Fig. 1

Source Code 2

Original MATLAB code used to solve for the dispersions and attenuations of SPhPs in Extended Data Fig. 1

Source data

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Pan, Z., Lu, G., Li, X. et al. Remarkable heat conduction mediated by non-equilibrium phonon polaritons. Nature 623, 307–312 (2023). https://doi.org/10.1038/s41586-023-06598-0

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