Abstract
The observation of second sound—a propagating wave-like manifestation of hydrodynamic heat transport—in solid crystals has been confined to a handful of materials at cryogenic temperatures, as disorder and Umklapp scattering suppress this phenomenon at room temperature. Here, we report the direct observation of second sound at ambient conditions in isotopically purified graphite. Using transient thermal grating spectroscopy, we measure a distinct damped oscillatory signal that provides unambiguous evidence of second sound, decisively distinguishing it from diffusive and ballistic transport regimes. This collective phonon dynamics enables an enhancement of the effective thermal conductivity, even surpassing the conventional diffusive limit by nearly 10%. Our work establishes the control of phonon-isotope scattering as a powerful strategy to unlock hydrodynamic phonon transport. It demonstrates that phonon hydrodynamics is an accessible and exploitable phenomenon in crystals at room temperature, providing an avenue for the fundamental study and application of wave-like heat transport.
Data availability
All data in the experiments and analysis that support the findings of this study are available. Source data are provided with this study.
References
Peshkov, V. Second sound in helium II. J. Phys. 8, 381–389 (1944).
Landau, L. Theory of the superfluidity of helium II. Phys. Rev. 60, 356–358 (1941).
Narayanamurti, V. & Dynes, R. C. Observation of second sound in bismuth. Phys. Rev. Lett. 28, 1461–1465 (1972).
McNelly, T. F. et al. Heat pulses in NaF: onset of second sound. Phys. Rev. Lett. 24, 100–102 (1970).
Huberman, S. et al. Observation of second sound in graphite at temperatures above 100 K. Science 364, 375–379 (2019).
Ding, Z. et al. Observation of second sound in graphite over 200. K. Nat. Commun. 13, 285 (2022).
Beardo, A. et al. Observation of second sound in a rapidly varying temperature field in Ge. Sci. Adv. 7, eabg4677 (2021).
Hardy, R. J. Phonon Boltzmann equation and second sound in solids. Phys. Rev. B 2, 1193–1207 (1970).
Enz, C. P. One-particle densities, thermal propagation, and second sound in dielectric crystals. Ann. Phys. 46, 114–173 (1968).
Cepellotti, A. et al. Phonon hydrodynamics in two-dimensional materials. Nat. Commun. 6, 6400 (2015).
Simoncelli, M., Marzari, N. & Cepellotti, A. Generalization of Fourier’s law into viscous heat equations. Phys. Rev. X 10, 011019 (2020).
Machida, Y., Matsumoto, N., Isono, T. & Behnia, K. Phonon hydrodynamics and ultrahigh-room-temperature thermal conductivity in thin graphite. Science 367, 309–312 (2020).
Huang, X. et al. Observation of phonon Poiseuille flow in isotopically purified graphite ribbons. Nat. Commun. 14, 2044 (2023).
Huang, X. et al. A graphite thermal Tesla valve driven by hydrodynamic phonon transport. Nature 634, 1086–1090 (2024).
Lee, S., Broido, D., Esfarjani, K. & Chen, G. Hydrodynamic phonon transport in suspended graphene. Nat. Commun. 6, 6290 (2015).
Chen, K. et al. Ultrahigh thermal conductivity in isotope-enriched cubic boron nitride. Science 367, 555–559 (2020).
Taniguchi, T. & Watanabe, K. Synthesis of high-purity boron nitride single crystals under high pressure by using Ba–BN solvent. J. Cryst. Growth 303, 525–529 (2007).
Hua, C. & Lindsay, L. Space-time dependent thermal conductivity in nonlocal thermal transport. Phys. Rev. B 102, 104310 (2020).
Chiloyan, V. et al. Green’s functions of the Boltzmann transport equation with the full scattering matrix for phonon nanoscale transport beyond the relaxation-time approximation. Phys. Rev. B 104, 245424 (2021).
Alofi, A. & Srivastava, G. P. Thermal conductivity of graphene and graphite. Phys. Rev. B 87, 115421 (2013).
Johnson, J. A. et al. Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys. Rev. Lett. 110, 025901 (2013).
Yan, Z. et al. Thermography of the superfluid transition in a strongly interacting Fermi gas. Science 383, 629–633 (2024).
Jaćimovski, S. K., Bukurov, M., Šetrajčić, J. P. & Raković, D. I. Phonon thermal conductivity of graphene. Superlattices Microstruct. 88, 330–337 (2015).
Balandin, A. A. & Nika, D. L. Phononics in low-dimensional materials. Mater. Today 15, 266–275 (2012).
Callaway, J. Model for lattice thermal conductivity at low temperatures. Phys. Rev. 113, 1046–1051 (1959).
Qian, X., Quan, G., Liu, T.-H. & Yang, R. API phonons: Python interfaces for phonon transport modeling. Mater. Today Phys. 50, 101630 (2025).
Qian, X., Zhang, C., Liu, T.-H. & Yang, R. Analytical Green’s function of the multidimensional Boltzmann transport equation for modeling hydrodynamic second sound. Phys. Rev. B 111, 035406 (2025).
Cattaneo, C. et al. Sulla conduzione del calore. Atti Semin. Mat. E Fis. Della Univ. Modena 3, 83–101 (1948).
Vernotte, P. et al. Les paradoxes de la théorie continue de l’équation de la chaleur. Comptes Rendus L’Acad. émie Sci. 246, 3154–3155 (1958).
Johnson, J. A. et al. Phase-controlled, heterodyne laser-induced transient grating measurements of thermal transport properties in opaque material. J. Appl. Phys. 111, 023503 (2012).
Choudhry, U. et al. Characterizing microscale energy transport in materials with transient grating spectroscopy. J. Appl. Phys. 130, 231101 (2021).
Maznev, A. A., Nelson, K. A. & Rogers, J. A. Optical heterodyne detection of laser-induced gratings. Opt. Lett. 23, 1319–1321 (1998).
Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).
Kresse, G., Furthmüller, J. & Hafner, J. Ab initio force constant approach to phonon dispersion relations of diamond and graphite. Europhys. Lett. 32, 729 (1995).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Klimeš, J., Bowler, D. R. & Michaelides, A. Chemical accuracy for the van der Waals density functional. J. Phys. Condens. Matter 22, 022201 (2009).
Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).
Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).
Li, W., Carrete, J., Katcho, N. A. & Mingo, N. ShengBTE: a solver of the Boltzmann transport equation for phonons. Comput. Phys. Commun. 185, 1747–1758 (2014).
Compte, A. & Metzler, R. The generalized Cattaneo equation for the description of anomalous transport processes. J. Phys. Math. Gen. 30, 7277 (1997).
Tateishi, A. A., Ribeiro, H. V. & Lenzi, E. K. The role of fractional time-derivative operators on anomalous diffusion. Front. Phys. 5, 52 (2017).
Galovic, S. et al. Electrical analogy approach to fractional heat conduction models. Fractal Fract. 9, 653 (2025).
Mainardi, F. et al. Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. https://doi.org/10.1142/p614 (IMPERIAL COLLEGE PRESS, 2010).
Isaeva, L., Barbalinardo, G., Donadio, D. & Baroni, S. Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach. Nat. Commun. 10, 3853 (2019).
Fiorentino, A. & Baroni, S. From Green-Kubo to the full Boltzmann kinetic approach to heat transport in crystals and glasses. Phys. Rev. B 107, 054311 (2023).
Ward, A., Broido, D. A., Stewart, D. A. & Deinzer, G. Ab initio theory of the lattice thermal conductivity in diamond. Phys. Rev. B 80, 125203 (2009).
Lindsay, L., Broido, D. A. & Mingo, N. Flexural phonons and thermal transport in graphene. Phys. Rev. B 82, 115427 (2010).
Joseph, D. D. & Preziosi, L. Heat waves. Rev. Mod. Phys. 61, 41–73 (1989).
Smith, G. S. Two velocities of sound in helium-II. Nature 157, 200–200 (1946).
Picard, S., Burns, D. T. & Roger, P. Determination of the specific heat capacity of a graphite sample using absolute and differential methods. Metrologia 44, 294 (2007).
Stern, M. J. et al. Mapping momentum-dependent electron-phonon coupling and nonequilibrium phonon dynamics with ultrafast electron diffuse scattering. Phys. Rev. B 97, 165416 (2018).
Kremeyer, L., Britt, T. L., Siwick, B. J. & Huberman, S. C. Ultrafast electron diffuse scattering as a tool for studying phonon transport: Phonon hydrodynamics and second sound oscillations. Struct. Dyn. 11, 024101 (2024).
Acknowledgements
This work was supported by projects National Key Research and Development Program of China No. 2023YFB4603801; National Natural Science Foundation of China No. 52176173 and No. 21FAA02809; Guangdong Innovative and Entrepreneurial Research Team Program No. 2021ZT09L227; Guang Dong Basic and Applied Basic Research Foundation No. 2020A1515110192, No. 2022A1515010710 and No. 2023B1515040023. The experiments reported were partially conducted at the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices. No. 2022B1212010008.
Author information
Authors and Affiliations
Contributions
Z.D., M.N. and Ke.C. conceived the idea; Z.X., Y.Z., Z.D., D.D., Ku.C., K.W., T.L., T.T., X.Q. and Ke.C. developed the methodology; Z.X., Y.Z., X.H., J.W., X.Q. and Ke.C. conducted the investigations; Z.X., Y.Z., X.H. and Ke.C. prepared the figures; Z.X., Y.Z., X.Q. and Ke.C. wrote the original draft; Z.X., Y.Z., X.H., Z.D., X.Q., M.N. and Ke.C. reviewed and edited the manuscript; T.L., M.N. and Ke.C. supervised the project; T.L. and Ke.C. acquired the funding; Ke.C. was responsible for project administration.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Xie, Z., Zhang, Y., Huang, X. et al. Room-temperature second sound in isotopically pure graphite. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70807-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-026-70807-3
