Graphene is predicted to be the two-dimensional material in which hydrodynamic phonon transport — including second sound, the damped wave-like propagation of heat — should survive at the highest temperatures, yet no experimental observation exists in monolayer graphene at room temperature and no quantitative regime map exists that couples the hydrodynamic window to branch-resolved electron–phonon energy transfer. Starting from the extended temperature model study of femtosecond laser heating of graphene (Rezgui, 2025), which explicitly lists 'phonon hydrodynamic transport at room temperature' as unresolved future work, this problem asks: for monolayer graphene at approximately 300 K, determine the regimes — in temperature in the vicinity of room temperature and in the electron–phonon channels (momentum-conserving normal versus disorder-assisted supercollision) — in which phonon hydrodynamic transport and its second-sound signatures persist, and those in which momentum-relaxing processes suppress them.

Background

Heat transport by lattice vibrations (phonons) crosses over between regimes set by the competition between momentum-conserving 'normal' (N) phonon–phonon collisions and momentum-relaxing collisions (Umklapp phonon–phonon processes, isotope and defect scattering, boundary/edge scattering, substrate coupling, and electron–phonon scattering). When normal collisions dominate, the phonon gas behaves collectively like a fluid: this is phonon hydrodynamics, whose observable signatures include Poiseuille-like heat flow (parabolic flux profiles, as in viscous pipe flow) and second sound — the damped oscillatory, wave-like propagation of temperature/heat at a speed between the diffusive and ballistic (collisionless free-flight) limits, first discussed by Peierls in 1929 and long confined in bulk crystals to cryogenic temperatures. The two-temperature model (TTM) is the standard macroscopic description of laser-heated metals and semimetals: electron and lattice temperatures coupled by a coupling factor GG, with diffusive (Fourier) heat flow. The extended temperature model (ETM) used in the source paper refines this by (i) resolving the lattice into separate phonon-branch temperatures for the longitudinal acoustic (LA), transverse acoustic (TA), and out-of-plane flexural (ZA) modes of graphene, and (ii) introducing thermal lag (dual-phase-lag heat-flux relaxation), which produces wave-like temperature dynamics beyond Fourier diffusion; it also splits the electron–phonon coupling into a momentum-conserving normal channel GepnG_{ep}^{n} and a supercollision channel GepSCG_{ep}^{SC}, where supercollisions are disorder- or ripple-assisted electron–phonon scattering events with large momentum transfer that bypass the momentum-conservation bottleneck of ordinary electron–phonon scattering and thereby enhance hot-electron cooling. The relevant diagnostic in experiments such as transient thermal grating (TTG) spectroscopy — where two crossed laser pulses create a sinusoidal temperature grating whose decay is monitored — is whether the response shows a damped oscillation (second sound) rather than purely diffusive or ballistic decay; the Knudsen number (ratio of phonon mean free path to sample length) and the ratio of normal to resistive scattering rates set the boundaries between these regimes, conventionally analyzed via the phonon Boltzmann (Peierls) transport equation, the standard kinetic equation for the phonon distribution. Prior results: first-principles calculations — phonon dispersions and scattering rates computed from density-functional theory without empirical parameters — (Lee et al. 2015; Cepellotti et al. 2015) predicted that suspended graphene supports hydrodynamic phonon transport — drift, Poiseuille flow, and second sound — at significantly higher temperatures and over wider temperature windows than bulk crystals. Experiments, however, have so far realized second sound only in bulk or layered-adjacent systems: graphite above 100 K (Huberman et al. 2019), transient hydrodynamic lattice cooling in graphite (Jeong et al. 2021), germanium (Beardo et al. 2021), graphite over 200 K (Ding et al. 2022), and most recently ambient-condition second sound in isotopically purified bulk graphite (Xie et al. 2026), where suppressing isotope (momentum-relaxing) scattering was the enabling strategy. For graphene itself, theory and simulation continue to advance — multiscale Boltzmann-equation simulations of second sound in graphene ribbons (Luo et al. 2019), hydrodynamic equations for generic 2D crystals (Scuracchio et al. 2019), analytic conditions for heat-flow waves in suspended graphene (Xu 2022), Green's-function modeling of hydrodynamic second sound (Qian et al. 2025), and molecular-dynamics studies (Martinez Margolles and Schelling 2026) predicting strong oscillatory, second-sound-like transport in graphene at 300 K but only for length scales of about 68 nm and below, with the lifetime governed by wave coherence tied to the phonon band structure — but no experiment has observed hydrodynamic second sound in monolayer graphene at room temperature, and the source paper itself notes that at room temperature the momentum conservation of normal scattering is not maintained, so that lattice cooling is dominated by the electron–phonon energy-transfer process. What is missing, and what the source paper's future-work sentence points to, is a quantitative determination of the room-temperature hydrodynamic window of graphene that includes the momentum-relaxing channels — including the branch-resolved electron–phonon and supercollision coupling that the ETM framework was built to resolve.

Problem Statement

For monolayer graphene at room temperature (approximately 300 K), determine the regimes in which phonon hydrodynamic transport and its second-sound signatures persist, and those in which they are suppressed by momentum-relaxing processes. Within a phonon-branch-resolved (LA/TA/ZA) treatment of the coupled electron–phonon system — the extended temperature model framework of the source paper, or an equivalent or more microscopic (Boltzmann-equation, molecular-dynamics, or first-principles) description — establish quantitatively how the hydrodynamic window around 300 K depends on: (i) temperature in the vicinity of room temperature; and (ii) the electron–phonon channels, i.e. the momentum-conserving normal coupling GepnG_{ep}^{n} versus the disorder-assisted supercollision coupling GepSCG_{ep}^{SC}. Because the location of the boundary between the hydrodynamic and momentum-relaxed regimes is itself part of what is to be determined, state explicitly and justify the operational criterion adopted for the edge of the hydrodynamic window (for example a stated threshold on the ratio of momentum-conserving to momentum-relaxing scattering rates, and/or on the Knudsen number, or the condition for a damped oscillation rather than a purely relaxational decay of the transient thermal grating). Give the window quantitatively as an explicit function of temperature across the interval mapped in the vicinity of room temperature, vary the two electron–phonon couplings GepnG_{ep}^{n} and GepSCG_{ep}^{SC} over their physically admissible range (independently and/or through their ratio), and state the sample conditions assumed (suspended or supported monolayer, and the length or geometry scale that fixes the Knudsen number).

References

  1. H. Rezgui, Giant enhancement of phonon–electron coupling in graphene under femtosecond laser heating at room temperature, Journal of Physics D: Applied Physics 58 (2025), DOI 10.1088/1361-6463/ade9d3, https://doi.org/10.1088/1361-6463/ade9d3; arXiv:2506.07114, https://arxiv.org/abs/2506.07114
  2. S. Lee, D. Broido, K. Esfarjani, G. Chen, Hydrodynamic phonon transport in suspended graphene, Nature Communications 6 (2015), DOI 10.1038/ncomms7290, https://doi.org/10.1038/ncomms7290
  3. A. Cepellotti, G. Fugallo, L. Paulatto, M. Lazzeri, F. Mauri, N. Marzari, Phonon hydrodynamics in two-dimensional materials, Nature Communications 6 (2015), DOI 10.1038/ncomms7400, https://doi.org/10.1038/ncomms7400
  4. S. Huberman, R. A. Duncan, K. Chen, B. Song, V. Chiloyan, Z. Ding, A. A. Maznev, G. Chen, K. A. Nelson, Observation of second sound in graphite at temperatures above 100 K, Science 364 (2019), DOI 10.1126/science.aav3548, https://doi.org/10.1126/science.aav3548
  5. J. Jeong, X. Li, S. Lee, L. Shi, Y. Wang, Transient hydrodynamic lattice cooling by picosecond laser irradiation of graphite, Physical Review Letters 127 (2021), DOI 10.1103/PhysRevLett.127.085901, https://doi.org/10.1103/PhysRevLett.127.085901
  6. A. Beardo, M. López-Suárez, L. A. Pérez, L. Sendra, M. I. Alonso, C. Melis, J. Bafaluy, J. Camacho, L. Colombo, R. Rurali, F. X. Alvarez, J. S. Reparaz, Observation of second sound in a rapidly varying temperature field in Ge, Science Advances 7 (2021), DOI 10.1126/sciadv.abg4677, https://doi.org/10.1126/sciadv.abg4677
  7. Z. Ding, K. Chen, B. Song, J. Shin, A. A. Maznev, K. A. Nelson, G. Chen, Observation of second sound in graphite over 200 K, Nature Communications 13 (2022), DOI 10.1038/s41467-021-27907-z, https://doi.org/10.1038/s41467-021-27907-z
  8. Z. Xie, Y. Zhang, X. Huang, Z. Ding, J. Wei, D. Dong, K. Cao, T. Lai, K. Watanabe, T. Taniguchi, X. Qian, M. Nomura, K. Chen, Room-temperature second sound in isotopically pure graphite, Nature Communications 17 (2026), DOI 10.1038/s41467-026-70807-3, https://doi.org/10.1038/s41467-026-70807-3
  9. X.-P. Luo, Y.-Y. Guo, M.-R. Wang, H.-L. Yi, Direct simulation of second sound in graphene by solving the phonon Boltzmann equation via a multiscale scheme, Physical Review B 100 (2019), DOI 10.1103/PhysRevB.100.155401, https://doi.org/10.1103/PhysRevB.100.155401; arXiv:1907.13277, https://arxiv.org/abs/1907.13277
  10. P. Scuracchio, K. H. Michel, F. M. Peeters, Phonon hydrodynamics, thermal conductivity, and second sound in two-dimensional crystals, Physical Review B 99 (2019), DOI 10.1103/PhysRevB.99.144303, https://doi.org/10.1103/PhysRevB.99.144303
  11. M. Xu, Heat flow wave in suspended graphene, Proceedings of the Royal Society A 478 (2022), DOI 10.1098/rspa.2022.0195, https://doi.org/10.1098/rspa.2022.0195
  12. X. Qian, C. Zhang, T.-H. Liu, R. Yang, Analytical Green's function of the multidimensional Boltzmann transport equation for modeling hydrodynamic second sound, Physical Review B 111 (2025), DOI 10.1103/PhysRevB.111.035406, https://doi.org/10.1103/PhysRevB.111.035406
  13. A. Martinez Margolles, P. K. Schelling, Thermal response functions and second sound in graphene, Journal of Applied Physics 139 (2026), DOI 10.1063/5.0317158, https://doi.org/10.1063/5.0317158; arXiv:2512.13988, https://arxiv.org/abs/2512.13988
  14. A. Martinez-Margolles, P. K. Schelling, Thermal-response functions and the Peierls–Boltzmann equation for second sound and phonon hydrodynamics in graphene, arXiv:2607.07644 (2026), https://arxiv.org/abs/2607.07644
  15. H. Rezgui, Phonon hydrodynamic transport: Observation of thermal wave-like flow and second sound propagation in graphene at 100 K, ACS Omega 8 (2023), DOI 10.1021/acsomega.3c02558, https://doi.org/10.1021/acsomega.3c02558
  16. H. Rezgui, C. Zhang, C. S. Sotomayor Torres, Extended multi-temperature model for electron–phonon coupling and ultrafast thermal transport in graphene, Applied Physics Letters 128 (2026), DOI 10.1063/5.0314469, https://doi.org/10.1063/5.0314469
  17. J.-W. Shen, X.-P. Luo, J.-Y. Xu, Y. Guo, H.-L. Yi, Phonon hydrodynamic transport in bilayer graphene, International Journal of Heat and Mass Transfer 247 (2025), DOI 10.1016/j.ijheatmasstransfer.2025.127086, https://doi.org/10.1016/j.ijheatmasstransfer.2025.127086