Experiments in 2020 measured near-field thermal radiation between two parallel quartz plates down to a 7 nm vacuum gap, finding an 18,000-fold enhancement over the blackbody limit in agreement with fluctuational electrodynamics (Salihoglu et al., Nano Lett. 2020). Whether fluctuational electrodynamics remains valid below this gap, and at what separation non-radiative channels such as phonon tunneling and contact-mediated transport become significant between flat surfaces, is still experimentally unresolved: no controlled parallel-plate measurement below ~7 nm existed as of August 2026, while sphere-plane and tip-plane experiments in the sub-10 nm regime give mutually contradictory results and atomistic simulations predict order-of-magnitude additional heat flux from phonon tunneling at 1-2 nm gaps. The problem is to extend controlled parallel-plate measurements into this extreme near-field regime, map the heat flux versus gap down toward contact for quartz and at least one other material system, and establish the gap scale and mechanism of the crossover from photon tunneling to non-radiative transport.

Background

When two bodies at different temperatures face each other across a vacuum gap, heat is carried by thermal (electromagnetic) radiation. Far apart, this transfer is bounded by the blackbody limit of Stefan and Boltzmann. At separations comparable to or smaller than the thermal wavelength (roughly 10 micrometers at room temperature), evanescent electromagnetic waves — fields bound to each surface that decay exponentially into the gap — can tunnel across, so the radiative heat flux can exceed the blackbody limit by orders of magnitude. For polar dielectrics such as quartz or silica the dominant carriers are surface phonon polaritons: collective modes in which infrared photons couple to lattice vibrations of the surface. The standard theory of this near-field radiative heat transfer is fluctuational electrodynamics, introduced by Polder and Van Hove in 1971, which treats thermal emission as arising from fluctuating currents and charges in each body and computes the radiative conductance between planar surfaces exactly; for two parallel planes the theory predicts a heat flux diverging roughly like the inverse square of the gap as the separation shrinks. Below gaps of about 10 nm — the 'extreme near field' — this prediction becomes questionable: real surfaces are atomically structured, electromagnetic nonlocality matters, and entirely non-radiative channels appear. In phonon tunneling, the lattice vibrations (phonons) of one solid excite those of the facing solid across a vacuum gap of nanometer or sub-nanometer width through the short-range electromagnetic interaction between the atoms, a mechanism absent from fluctuational electrodynamics, which accounts only for photon-mediated transfer. Extreme-near-field experiments performed so far used a sphere facing a plate, or a sharp tip facing a plate, because such geometries avoid the jump-to-contact (snap-in) instability in which Casimir and van der Waals attraction pulls two extended parallel plates into contact below a critical gap. These non-planar results disagree with one another: a silica sphere-plate experiment down to roughly 1 nm observed a saturation plateau (Kim et al., Nature 2015); a gold tip-plate experiment at 0.2-7 nm measured fluxes four orders of magnitude above fluctuational-electrodynamics predictions and not explained by phonon-tunneling theories available at the time (Kloppstech et al., Nat. Commun. 2017); and gold sphere-plate measurements agreed with the theory down to the saturation regime near tens of nanometers (Rincón-García et al., PRL 2022), while the most recent sphere-film measurement found fluxes about 100 times above the theory below 10 nm (Geesmann et al., PRL 2025). A decisive difficulty is that in sphere-plane and tip-plane geometries the effective transfer area at the smallest gaps is ill-defined — a nanoscale contact region of uncertain shape — so the excess flux may reflect geometry rather than new physics. Parallel plates have no such ambiguity: the fluctuational-electrodynamics prediction for two flat surfaces is exact and curvature-free, which is precisely why the 2020 quartz plate-plate measurement down to 7 nm (18,000-fold enhancement over the blackbody limit, agreeing with theory) is regarded as the cleanest test to date, and why its extension below 7 nm — blocked in practice by the need for sub-nanometer roughness, sub-microradian parallelism, and control of the jump-to-contact instability, and requiring embedded microfabricated thermometers sensitive to pico- to nanowatt heat flows — is the outstanding step. On the theory side, nonequilibrium molecular dynamics and first-principles calculations now make concrete predictions for the extreme near field between flat silica and other polar dielectrics: roughly a thirtyfold further increase of the heat-transfer coefficient at a 2 nm gap relative to 10 nm, with deviations from fluctuational electrodynamics at still smaller gaps attributed to acoustic phonon tunneling and to surface-region variations of the dielectric permittivity (Rajabpour et al., APL 2024; Guo et al., PRB 2023; Tokunaga et al., PRB 2022).

Problem Statement

Experimentally determine the heat transfer between two parallel plates separated by vacuum gaps below the 7 nm bound reached in 2020, extending toward the contact regime, and thereby answer two linked questions for flat surfaces: (i) does fluctuational electrodynamics quantitatively predict the heat flux between parallel plates in the extreme near field below about 10 nm, as it does at 7 nm and above for quartz, or does it fail as several sphere-plane and tip-plane measurements suggest; and (ii) at what gap scale, and through which mechanism, do non-radiative channels — phonon tunneling and contact-mediated transport — become significant relative to photon tunneling, reaching the photon-tunneling to non-radiative crossover at which the non-radiative contribution equals the photon-tunneling contribution, as predicted by atomistic simulations to occur at gaps of a few nanometers and below? For flat surfaces this regime is reachable only with a controlled parallel-plate measurement platform that maintains parallelism and avoids jump-to-contact at sub-7 nm gaps, with the repeatability and uncertainty sufficient to discriminate between the competing predictions; what settles (i) and (ii) is the measured heat flux or thermal conductance as a function of gap, from overlap with the existing 7 nm data down toward the smallest achievable gap (including the contact/sub-nanometer limit and the dynamics of the jump itself, which may mask or reveal additional channels), compared against the fluctuational-electrodynamics prediction and with surface roughness and parasitic heat paths quantified so that the radiative and non-radiative contributions can be separated. The comparison covers quartz and at least one additional material system (another polar dielectric, a metal, or a structured surface such as a metasurface), and the crossover it reveals — the gap scale and mechanism at which the non-radiative contribution equals photon tunneling — establishes whether the observed gap dependence and crossover are material-dependent.

References

  1. Hakan Salihoglu, Woongsik Nam, Luis Traverso, Mauricio Segovia, Prabhu K. Venuthurumilli, Wen Liu, Yu Wei, Wenjuan Li, Xianfan Xu, 'Near-Field Thermal Radiation between Two Plates with Sub-10 nm Vacuum Separation', Nano Letters 20, 6091-6096 (2020), DOI 10.1021/acs.nanolett.0c02137, https://doi.org/10.1021/acs.nanolett.0c02137
  2. D. Polder, 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. 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
  4. 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
  5. Laura Rincón-García, Dakotah Thompson, Rohith Mittapally, Nicolás Agraït, Edgar Meyhofer, Pramod Reddy, 'Enhancement and Saturation of Near-Field Radiative Heat Transfer in Nanogaps between Metallic Surfaces', Physical Review Letters 129, 145901 (2022), DOI 10.1103/PhysRevLett.129.145901, https://doi.org/10.1103/PhysRevLett.129.145901
  6. 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 (2025), DOI 10.1103/lcz1-f5v9, arXiv:2505.01723, https://doi.org/10.1103/lcz1-f5v9
  7. Takuro Tokunaga, Masao Arai, Kazuaki Kobayashi, Wataru Hayami, Shigeru Suehara, Takuma Shiga, Keunhan Park, Mathieu Francoeur, 'First-principles calculations of phonon transport across a vacuum gap', Physical Review B 105, 045410 (2022), DOI 10.1103/PhysRevB.105.045410, https://doi.org/10.1103/PhysRevB.105.045410
  8. 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
  9. 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
  10. Rohith Mittapally, Ju Won Lim, Lang Zhang, Owen D. Miller, Pramod Reddy, Edgar Meyhofer, 'Probing the Limits to Near-Field Heat Transfer Enhancements in Phonon-Polaritonic Materials', Nano Letters 23, 2187-2194 (2023), DOI 10.1021/acs.nanolett.2c04735, https://doi.org/10.1021/acs.nanolett.2c04735
  11. Zexiao Wang, Renwen Yu, Hakan Salihoglu, Xiao Luo, Zhuo Li, Hyeonggyun Kim, Xiu Liu, Tianyi Huang, Yibai Zhong, Shanhui Fan, Sheng Shen, 'Metamaterial-enhanced near-field radiative heat transfer', Nature 654, 64-68 (2026), DOI 10.1038/s41586-026-10595-4, https://doi.org/10.1038/s41586-026-10595-4
  12. Christophe Lucchesi, Rodolphe Vaillon, Pierre-Olivier Chapuis, 'Radiative heat transfer at the nanoscale: experimental trends and challenges', Nanoscale Horizons 6, 201-208 (2021), DOI 10.1039/d0nh00609b, https://doi.org/10.1039/d0nh00609b