Near-field radiative heat transfer (NFRHT) between solid surfaces separated by vacuum gaps smaller than the thermal photon wavelength is dominated by evanescent electromagnetic modes and exceeds the blackbody limit by orders of magnitude. The landmark measurements of Kim et al. (Nature 528, 387–391, 2015) confirmed down to gaps of ~2–3 nm that local fluctuational electrodynamics (FE), combined with realistic geometry and roughness, quantitatively predicts this transfer for both dielectric and metal surfaces, and posed the still-unresolved question of what happens at smaller separations. The open problem is to determine, experimentally and theoretically, the mechanism(s) and magnitude of heat transfer across vacuum gaps from a few nanometres down to atomic contact: the validity limit of local FE below a few nanometres, the crossover to non-radiative channels such as phonon tunnelling and electronic transport, and the role of spatial dispersion and of correlations between the thermal fluctuations of the two surfaces. The question is live and contested: recent clean-condition experiments disagree by orders of magnitude, anomalous signals in metallic gaps have been traced to water menisci, atomistic simulations predict a phonon-tunnelling crossover for polar dielectrics that remains untested below ~1 nm, and a 2026 theory argues that FE itself breaks down at sub-nanometre gaps.

Background

Radiative heat transfer between two bodies at different temperatures is described at the macroscale by the Stefan–Boltzmann law, but when the separation dd becomes comparable to or smaller than the thermal photon wavelength (roughly 10 µm at room temperature), evanescent electromagnetic waves that do not propagate to the far field dominate the exchange. Polder and Van Hove (1971) formulated the standard theoretical framework, fluctuational electrodynamics (FE): each body emits thermal radiation generated by fluctuating currents whose correlations are fixed by the fluctuation–dissipation theorem, and the heat flux follows from the scattering of these fields between the two bodies. For polar dielectrics and metals, surface electromagnetic resonances (surface phonon polaritons and surface plasmon polaritons — evanescent electromagnetic modes bound to each interface) resonantly enhance the transfer, which scales approximately as 1/d21/d^{2} and can exceed the blackbody limit by several orders of magnitude. Because these resonances occur at nanometre distances, this 'extreme near field' (gaps below roughly 10 nm) is both technologically relevant — for near-field thermophotovoltaics, heat-assisted magnetic recording, and scanning thermal probes — and experimentally difficult, since surface forces cause snap-in (the sudden adhesive jump of a probe into contact) and thermally induced deflections destabilize the smallest gaps. Kim et al. (Nature 528, 387–391, 2015) overcame these difficulties with a custom bimaterial cantilever serving as both thermal sensor and actuator, measuring radiative heat transfer between silica–silica and gold–gold pairs down to gaps of ~2 nm (dielectric) and ~3 nm (metal), and showed that local FE with realistic tip geometry and roughness reproduces the data quantitatively. However, local FE rests on two assumptions expected to fail at small separations: that the dielectric response is local (no spatial dispersion, i.e., no dependence of the dielectric function on wavevector, which becomes relevant when field gradients reach atomic length scales), and that the thermal fluctuations in the two bodies are statistically independent. Moreover, at gaps approaching the interatomic spacing, non-radiative channels that FE does not describe become possible: phonon tunnelling (the coupling of lattice vibrations of one solid to the other through the evanescent electromagnetic field or across the vacuum gap), and electronic heat transport via wavefunction overlap or electron tunnelling. Whether local FE survives below a few nanometres, and how photon-mediated transfer crosses over to these non-radiative mechanisms, is precisely the frontier identified by Kim et al. and remains unsettled.

Problem Statement

Determine the mechanism(s), magnitude, and gap dependence of heat transfer between solid surfaces separated by vacuum gaps in the extreme near field — from a few nanometres down to atomic contact (separations of order the interatomic spacing, where electronic transport via wavefunction overlap or electron tunnelling becomes possible) — and thereby establish the validity limit of local fluctuational electrodynamics. Concretely: (1) measure heat flux or thermal conductance versus gap below ~2 nm, for both metallic and polar-dielectric material pairs, under experimentally demonstrated exclusion of contamination (water menisci, adsorbate bridges) and with independent gap metrology, deciding whether local FE quantitatively predicts the transfer or fails as some clean-condition experiments report; (2) identify and quantify the crossover from photon-mediated (evanescent electromagnetic) transfer to non-radiative channels — phonon tunnelling and electronic transport or wavefunction overlap — including the gap scale at which each channel dominates; and (3) supply the corresponding predictive theory, incorporating whatever physics beyond local FE is required (spatial dispersion of the dielectric response, correlations between the fluctuating currents of the two bodies, atomistic surface detail), validated against the clean-condition data. These components jointly serve one objective: establishing where local fluctuational electrodynamics ceases to be valid below a few nanometres and how heat transfer crosses over to non-radiative channels.

References

  1. Kyeongtae Kim, Bai Song, Víctor Fernández-Hurtado, Woochul Lee, Wonho Jeong, Longji Cui, Dakotah Thompson, Johannes Feist, M. T. Homer Reid, Francisco J. García-Vidal, Juan Carlos Cuevas, Edgar Meyhofer, Pramod Reddy, 'Radiative heat transfer in the extreme near field', Nature 528, 387–391 (2015). DOI: 10.1038/nature16070, https://doi.org/10.1038/nature16070
  2. D. Polder and M. Van Hove, 'Theory of Radiative Heat Transfer between Closely Spaced Bodies', Physical Review B 4, 3303–3314 (1971). DOI: 10.1103/PhysRevB.4.3303, https://doi.org/10.1103/PhysRevB.4.3303
  3. Pierre-Olivier Chapuis, Sebastian Volz, Carsten Henkel, Karl Joulain, Jean-Jacques Greffet, 'Effects of spatial dispersion in near-field radiative heat transfer between two parallel metallic surfaces', Physical Review B 77, 035431 (2008). DOI: 10.1103/PhysRevB.77.035431, https://doi.org/10.1103/PhysRevB.77.035431
  4. Vazrik Chiloyan, Jivtesh Garg, Keivan Esfarjani, Gang Chen, 'Transition from near-field thermal radiation to phonon heat conduction at sub-nanometre gaps', Nature Communications 6, 6755 (2015). DOI: 10.1038/ncomms7755, https://doi.org/10.1038/ncomms7755
  5. Konstantin Kloppstech, Nils Könne, Svend-Age Biehs, Alejandro W. Rodriguez, Ludwig Worbes, David Hellmann, Achim Kittel, 'Giant heat transfer in the crossover regime between conduction and radiation', Nature Communications 8, 14475 (2017). DOI: 10.1038/ncomms14475, https://doi.org/10.1038/ncomms14475
  6. Longji Cui, Wonho Jeong, Víctor Fernández-Hurtado, Johannes Feist, Francisco J. García-Vidal, Juan Carlos Cuevas, Edgar Meyhofer, Pramod Reddy, 'Study of radiative heat transfer in Ångström- and nanometre-sized gaps', Nature Communications 8, 14479 (2017). DOI: 10.1038/ncomms14479, https://doi.org/10.1038/ncomms14479
  7. Yangyu Guo, Mauricio Gómez Viloria, Riccardo Messina, Philippe Ben-Abdallah, Samy Merabia, 'Atomistic modeling of extreme near-field heat transport across nanogaps between two polar dielectric materials', Physical Review B 108, 085434 (2023). DOI: 10.1103/PhysRevB.108.085434, https://doi.org/10.1103/PhysRevB.108.085434
  8. Ali Rajabpour, Julien El Hajj, Mauricio Gómez Viloria, Riccardo Messina, Philippe Ben-Abdallah, Yangyu Guo, Samy Merabia, 'Extreme near-field heat transfer between silica surfaces', Applied Physics Letters 124, 192203 (2024). DOI: 10.1063/5.0203074, https://doi.org/10.1063/5.0203074
  9. Fridolin Geesmann, Philipp Thurau, Sophie Rodehutskors, Till Ziehm, Ludwig Worbes, Svend-Age Biehs, Achim Kittel, 'Transition from Near-Field to Extreme Near-Field Radiative Heat Transfer', Physical Review Letters 135, 166202 (2025). DOI: 10.1103/lcz1-f5v9, https://doi.org/10.1103/lcz1-f5v9 (preprint: arXiv:2505.01723, https://arxiv.org/abs/2505.01723)
  10. Rubén López-Nebreda, Oscar Mateos-Lopez, Pablo Martinez Martinez, Juan José García-Esteban, Ángel Ibabe, Nuria Roca-Giménez, Pilar Segovia, Enrique Garcia Michel, Eduardo J. H. Lee, Jose Guilherme Vilhena, Juan Carlos Cuevas, Nicolás Agraït, 'Heat transfer in metallic nanometre-sized gaps', Nature Communications 16, 7342 (2025). DOI: 10.1038/s41467-025-62672-3, https://doi.org/10.1038/s41467-025-62672-3
  11. Philippe Ben-Abdallah, 'Breakdown of Fluctuational Electrodynamics in the Extreme Near Field', arXiv:2606.05845 (2026). arXiv:2606.05845, https://arxiv.org/abs/2606.05845