Ballistic Phonons in Ultrathin Nanowires

Daniel Vakulov, Subash Gireesan, Milo Y. Swinkels, Ruben Chavez, Tom Vogelaar, Pol Torres, Alessio Campo, Marta De Luca, Marcel A. Verheijen, Sebastian Koelling, Luca Gagliano, Jos E.M. Haverkort, F. Xavier Alvarez, Peter A. Bobbert, Ilaria Zardo, Erik P.A.M. Bakkers (Corresponding author)

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According to Fourier's law, a temperature difference across a material results in a linear temperature profile and a thermal conductance that decreases inversely proportional to the system length. These are the hallmarks of diffusive heat flow. Here, we report heat flow in ultrathin (25 nm) GaP nanowires in the absence of a temperature gradient within the wire and find that the heat conductance is independent of wire length. These observations deviate from Fourier's law and are direct proof of ballistic heat flow, persisting for wire lengths up to at least 15 μm at room temperature. When doubling the wire diameter, a remarkably sudden transition to diffusive heat flow is observed. The ballistic heat flow in the ultrathin wires can be modeled within Landauer's formalism by ballistic phonons with an extraordinarily long mean free path.

Original languageEnglish
Pages (from-to)2703-2709
Number of pages7
JournalNano Letters
Issue number4
Publication statusPublished - 8 Apr 2020


We would like to acknowledge Rob van der Heijden, Riccardo Rurali, Michel de Jong, Bernd Gotsmann, Ali Shakouri, and Chris Palmstrøm for valuable feedback on the manuscript. This work has been supported by the European Research Council (ERC 617256 and 756365), the Dutch Organization for Scientific Research (NWO), the Foundation for Fundamental Research on Matter (FOM), and the Swiss National Science Foundation research grant (project grant no. 165784). We acknowledge Solliance, a solar energy R&D initiative of ECN, TNO, Holst, TU/e, imec and Forschungszentrum Jülich, and the Dutch province of Noord-Brabant for funding the TEM facility. This work is part of the Industrial Partnership Programme (IPP) “Computational sciences for energy research” of The Netherlands Organization for Scientific Research Institutes (NWO-I). This research program is co-financed by Shell Global Solutions International B.V. We acknowledge financial support by the Spain’s Ministerio de Ciencia, Innovacion y Universidades under grant No. RTI2018-097876-B-C21 (MCIU/AEI/FEDER, UE).

FundersFunder number
Dutch Organization for Scientific Research
Province of Noord-Brabant
Research Centre Julich (FZJ)
Ministerio de Ciencia e InnovaciónRTI2018-097876-B-C21
Horizon 2020 Framework Programme756365
European Research CouncilERC 617256
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung165784
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Stichting voor Fundamenteel Onderzoek der Materie


    • ballistic phonons
    • GaP
    • heat transport
    • Nanowires
    • Raman spectroscopy


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