Abstract
We measure the temperature profile and investigate the thermal conductivity of suspended monoisotopic hexagonal boron nitride (h10BN) heterostructures by combining suspended microbridge technique and Raman spectroscopy. The thermal conductivities exceed 1650 W.m−1.K−1 at room temperature, significantly higher than in previous reports, highlighting the crucial influence of the measurement conditions on the experimental results. By including more data points, we refine our models beyond the accuracy of conventional approaches. Our results show a striking deviation of thermal transport from the classical diffusion regime described by Fourier’s law: while the temperature profiles are linear above 300 K, they become clearly nonlinear below this temperature, indicating a strong non-diffusive heat transport regime. This behavior underscores the need for a new theoretical framework to fully account for heat transport in two-dimensional materials. Ultimately, our findings pave the way for innovative heat dissipation technologies and challenge conventional paradigms in nano-heat engineering. This study establishes a practical framework linking Raman-based temperature mapping, the number of measurement points, and thermal simulations to reliably determine the in-plane thermal conductivity of 2D materials.
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The data that support the findings of this study are available from the corresponding author. They are no restrictions to accessing data. The Comsol simulation are provided in the Supplementary Information section. Source data are provided with this paper.
References
Qian, X., Zhou, J. & Chen, G. Phonon-engineered extreme thermal conductivity materials. Nat. Mater. 20, 1188–1202 (2021).
Rahimi, M. et al. Complete determination of thermoelectric and thermal properties of supported few-layer two-dimensional materials. Phys. Rev. Appl. 19, 034075 (2023).
Rahimi, M. et al. Probing the electric and thermoelectric response of ferroelectric 2H and 3R α-In2Se3. Appl. Phys. Lett. 124, 253503 (2024).
Li, D. et al. Recent progress of two-dimensional thermoelectric materials. Nano-Micro Lett. 12, 36 (2020).
Kim, S. E. et al. Extremely anisotropic van der Waals thermal conductors. Nature 597, 660–665 (2021).
Huang, X. et al. A graphite thermal Tesla valve driven by hydrodynamic phonon transport. Nature 634, 1086–1090 (2024).
Vaziri, S. et al. Ultrahigh thermal isolation across heterogeneously layered two-dimensional materials. Sci. Adv. 5, eaax1325 (2019).
Lu, S. et al. Towards n-type conductivity in hexagonal boron nitride. Nat. Commun. 13, 3109 (2022).
Cai, Q. et al. Outstanding thermal conductivity of single atomic layer isotope-modified boron nitride. Phys. Rev. Lett. 125, 085902 (2020).
Cepellotti, A. et al. Phonon hydrodynamics in two-dimensional materials. Nat. Commun. 6, 6400 (2015).
Lee, S., Broido, D., Esfarjani, K. & Chen, G. Hydrodynamic phonon transport in suspended graphene. Nat. Commun. 6, 6290 (2015).
Fugallo, G. et al. Thermal conductivity of graphene and graphite: collective excitations and mean free paths. Nano Lett. 14, 6109–6114 (2014).
Huberman, S. et al. Observation of second sound in graphite at temperatures above 100 K. Science 364, 375–379 (2019).
Rezgui, H. Phonon hydrodynamic transport: observation of thermal wave-like flow and second sound propagation in graphene at 100 K. ACS Omega 8, 23964–23974 (2023).
Ding, Z. et al. Phonon hydrodynamic heat conduction and knudsen minimum in graphite. Nano Lett. 18, 638–649 (2018).
Machida, Y. et al. Observation of Poiseuille flow of phonons in black phosphorus. Sci. Adv. 4, eaat3374 (2018).
Srivastav, S. K. et al. Universal quantized thermal conductance in graphene. Sci. Adv. 5, eaaw5798 (2019).
Phonon hydrodynamics in bulk insulators and semimetals | Low Temperature Physics | AIP Publishing. https://pubs-aip-org.ezproxy.universite-paris-saclay.fr/aip/ltp/article/50/7/574/3303895/Phonon-hydrodynamics-in-bulk-insulators-and.
Jo, I. et al. Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride. Nano Lett. 13, 550–554 (2013).
Yuan, C. et al. Modulating the thermal conductivity in hexagonal boron nitride via controlled boron isotope concentration. Commun. Phys. 2, 1–8 (2019).
Mercado, E. et al. Isotopically enhanced thermal conductivity in few-layer hexagonal boron nitride: implications for thermal management. ACS Appl. Nano Mater. 3, 12148–12156 (2020).
Kim, Y. D. et al. Bright visible light emission from graphene. Nat. Nanotechnol. 10, 676–681 (2015).
Dobusch, L., Schuler, S., Perebeinos, V. & Mueller, T. Thermal light emission from monolayer MoS2. Adv. Mater. 29, 1701304 (2017).
Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008).
Braun, O. et al. Spatially mapping thermal transport in graphene by an opto-thermal method. Npj 2D Mater. Appl. 6, 1–7 (2022).
Taube, A., Judek, J., Łapińska, A. & Zdrojek, M. Temperature-dependent thermal properties of supported MoS2 monolayers. ACS Appl. Mater. Interfaces 7, 5061–5065 (2015).
Cai, W. et al. Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition. Nano Lett. 10, 1645–1651 (2010).
Machida, Y., Matsumoto, N., Isono, T. & Behnia, K. Phonon hydrodynamics and ultrahigh–room-temperature thermal conductivity in thin graphite. Science 367, 309–312 (2020).
Fong, K. C. & Schwab, K. C. Ultrasensitive and wide-bandwidth thermal measurements of graphene at low temperatures. Phys. Rev. X 2, 031006 (2012).
Mecklenburg, M. et al. Nanoscale temperature mapping in operating microelectronic devices. Science 347, 629–632 (2015).
Castioni, F. et al. Nanosecond nanothermometry in an electron microscope. Nano Lett. 25, 1601–1608 (2025).
Menges, F. et al. Temperature mapping of operating nanoscale devices by scanning probe thermometry. Nat. Commun. 7, 10874 (2016).
Eloïse, G. et al. Scanning thermal microscopy on samples of varying effective thermal conductivities and identical flat surfaces. J. Appl. Phys. 128, 235301 (2020).
Morell, N. et al. Optomechanical measurement of thermal transport in two-dimensional MoSe2 lattices. Nano Lett. 19, 3143–3150 (2019).
Chiout, A. et al. Extreme mechanical tunability in suspended MoS2 resonator controlled by Joule heating. npj 2D Mater. Appl. 7, 1–8 (2023).
Blaikie, A., Miller, D. & Alemán, B. J. A fast and sensitive room-temperature graphene nanomechanical bolometer. Nat. Commun. 10, 4726 (2019).
Kloppstech, K. et al. Giant heat transfer in the crossover regime between conduction and radiation. Nat. Commun. 8, 14475 (2017).
Majumdar, A., Chowdhury, S. & Ahuja, R. Ultralow thermal conductivity and high thermoelectric figure of merit in two-dimensional thallium selenide. ACS Appl. Energy Mater. 3, 9315–9325 (2020).
Zhao, J. et al. Graphene microheater chips for in situ TEM. Nano Lett. 23, 726–734 (2023).
Vakulov, D. et al. Ballistic phonons in ultrathin nanowires. Nano Lett. 20, 2703–2709 (2020).
Vincent, P. et al. Observations of the synthesis of straight single wall carbon nanotubes directed by electric fields in an environmental transmission electron microscope. Carbon 213, 118272 (2023).
Panciera, F. et al. Controlling nanowire growth through electric field-induced deformation of the catalyst droplet. Nat. Commun. 7, 12271 (2016).
Lee, J. E., Ahn, G., Shim, J., Lee, Y. S. & Ryu, S. Optical separation of mechanical strain from charge doping in graphene. Nat. Commun. 3, 1024 (2012).
Chaste, J. et al. Intrinsic properties of suspended MoS2 on SiO2/Si pillar arrays for nanomechanics and optics. ACS Nano 12, 3235–3242 (2018).
Chen, S. et al. Thermal conductivity of isotopically modified graphene. Nat. Mater. 11, 203–207 (2012).
Blundo, E. et al. Vibrational properties in highly strained hexagonal boron nitride bubbles. Nano Lett. 22, 1525–1533 (2022).
Dadgar, A. M. et al. Strain engineering and raman spectroscopy of monolayer transition metal dichalcogenides. Chem. Mater. https://doi.org/10.1021/acs.chemmater.8b01672 (2018).
Chiout, A. et al. High strain engineering of a suspended wsse monolayer membrane by indentation and measured by tip-enhanced photoluminescence. Adv. Opt. Mater. 12, 2302369 (2024).
Fulkerson, W., Moore, J. P., Williams, R. K., Graves, R. S. & McElroy, D. L. Thermal conductivity, electrical resistivity, and seebeck coefficient of silicon from 100 to 1300. K. Phys. Rev. 167, 765–782 (1968).
Shanks, H. R., Maycock, P. D., Sidles, P. H. & Danielson, G. C. Thermal conductivity of silicon from 300 to 1400°K. Phys. Rev. 130, 1743–1748 (1963).
Cai, Q. et al. High thermal conductivity of high-quality monolayer boron nitride and its thermal expansion. Sci. Adv. 5, eaav0129 (2019).
Xiao, P. et al. MoS2 phononic crystals for advanced thermal management. Sci. Adv. 10, eadm8825 (2024).
Schilling, A., Zhang, X. & Bossen, O. Heat flowing from cold to hot without external intervention by using a “thermal inductor”. Sci. Adv. 5, eaat9953 (2019).
Li, X. & Lee, S. Role of hydrodynamic viscosity on phonon transport in suspended graphene. Phys. Rev. B 97, 094309 (2018).
Liu, S. et al. Single crystal growth of millimeter-sized monoisotopic hexagonal boron nitride. Chem. Mater. 30, 6222–6225 (2018).
Acknowledgements
We thank Anis Chiout, Jérôme Saint-Martin and Michele Lazzeri for fruitfull discussion. The work was supported, by French grants ANR ANETHUM (ANR-19-CE24-0021, J.C.), ANR Deus-nano (ANR-19-CE42-0005, J.C.), ANR 2DHeco (ANR-20-CE05-0045, J.C.), ANR Comodes (ANR-22-CE09-0021, J.C.)), ANR ELEPHANT (ANR-21-CE30-0012-01, J.C.), and (ANR-22-PEXD-0006, J.C.) FastNano project, as well as the French technological network RENATECH, J.C. Support for the monoisotopic hBN crystal growth and was provided by the USA Office f Naval Research award N00014-22-1-2582 (J.H.E.).
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J.C. and A.O. initiated the work. C.B.-R. fabricated the 2D heterostructures, developed the soft 2D transfer and did the measurements with calibration. C.W. and F.P. fabricated the microheater. T.P. and J.H.E. have grown the isotopic hBN samples with the help of B.G. and G.C. G.D.B. and F.O. have grown the CVD WSe2 flakes. M.L.D. proceeded to the thermal reflectance measurements. C.B.-R., S.S., N.B., and L.M. are responsible for the graphene sample and measurements. C.B.-R., J.C., and E.H. did the PDMS 2D stamp and sample preparation. J.C. guided the research and wrote the manuscript with the input from all the authors.
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Brochard-Richard, C., Di Berardino, G., Herth, E. et al. Extreme longitudinal thermal conductivity and non-diffusive heat transport in isotopic hBN. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69907-x
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DOI: https://doi.org/10.1038/s41467-026-69907-x
