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# Observation of superdiffusive phonon transport in aligned atomic chains

## Abstract

Fascinating phenomena can occur as charge and/or energy carriers are confined in one dimension1,2,3,4. One such example is the divergent thermal conductivity (κ) of one-dimensional lattices, even in the presence of anharmonic interatomic interactions—a direct consequence of the Fermi–Pasta–Ulam–Tsingou paradox proposed in 19555. This length dependence of κ, also known as superdiffusive phonon transport, presents a classical anomaly of continued interest6,7,8,9. So far the concept has remained purely theoretical, because isolated single atomic chains of sufficient length have been experimentally unattainable. Here we report on the observation of a length-dependent κ extending over 42.5 µm at room temperature for ultrathin van der Waals crystal NbSe3 nanowires. We found that κ follows a 1/3 power law with wire length, which provides experimental evidence pointing towards superdiffusive phonon transport. Contrary to the classical size effect due to phonon-boundary scattering, the observed κ shows a 25-fold enhancement as the characteristic size of the nanowires decreases from 26 to 6.8 nm while displaying a normal–superdiffusive transition. Our analysis indicates that these intriguing observations stem from the transport of one-dimensional phonons excited as a result of elastic stiffening with a fivefold enhancement of Young’s modulus. The persistent divergent trend of the observed thermal conductivity with sample length reveals a real possibility of creating novel van der Waals crystal-based thermal superconductors with κ values higher than those of any known materials.

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## Data availability

Data are available from figshare at https://doi.org/10.6084/m9.figshare.14055413.

## Code availability

The code that has been used for this work is available from the corresponding author on request.

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## Acknowledgements

We thank the National Science Foundation (NSF) for financial support under grants DMR-1532107 and CBET-1805924. The financial support for sample preparation was provided by the National Science Foundation through the Penn State 2D Crystal Consortium-Materials Innovation Platform (2DCC-MIP) under National Science Foundation cooperative agreement DMR-1539916. Z.M. acknowledges support from the National Science Foundation under grant DMR-1917579. This work was performed in part at the Cornell NanoScale Facility, a National Nanotechnology Coordinated Infrastructure (NNCI) member supported by NSF grant NNCI-2025233.

## Author information

Authors

### Contributions

L.Y. conducted the transport property and Young’s modulus measurements. Y.T. and L.Y. performed the theoretical simulation. L.Y. and Z.P. performed sample preparation for the TEM studies. Y. Zhao and L.Y. fabricated the measurement microdevices. Y. Zhu and Z.M. synthesized the material. M.A. and K.W. performed the TEM characterizations. L.Y. and D.L. compiled and analysed the results. D.L. conceived and directed the project. L.Y. and D.L. wrote the manuscript with input from all authors.

### Corresponding author

Correspondence to Deyu Li.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Nanotechnology thanks Bernd Gotsmann, Yongjie Hu and Dvira Segal for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–19 and Notes 1–10.

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Reprints and Permissions

Yang, L., Tao, Y., Zhu, Y. et al. Observation of superdiffusive phonon transport in aligned atomic chains. Nat. Nanotechnol. 16, 764–768 (2021). https://doi.org/10.1038/s41565-021-00884-6

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