When two solid objects are separated by a vacuum gap of a few nanometres down to atomic spacings, heat crosses the gap by several concurrent channels: near-field thermal radiation (evanescent electromagnetic waves), phonon tunnelling, and, in metals, electron tunnelling. The source paper on coupled conductive and near-field radiative heat transfer between planar bodies (Messina, Jin and Rodriguez, Phys. Rev. B 94, 121410(R) (2016)) notes that at atomistic separations continuum fluctuational electrodynamics and Fourier conduction both fail and the boundary between radiative and phonon-mediated transfer is blurred, leaving a consistent microscopic theory bridging these channels unresolved.

Background

Radiative heat transfer (RHT) between objects hotter than their surroundings is classically bounded by Planck's blackbody law, but when the separation dd becomes smaller than the thermal wavelength (about 10 micrometres at room temperature), evanescent electromagnetic waves tunneling across the gap make the exchanged flux grow far beyond that bound. This near-field radiative heat transfer is described by fluctuational electrodynamics (FE), the framework of Rytov, Polder and van Hove: thermally fluctuating microscopic currents, with correlations fixed by the fluctuation-dissipation theorem, radiate through a continuum medium whose response is encoded in a local, frequency-dependent dielectric function. FE predicts a divergence of the flux roughly as 1/d21/d^2 as d→0d \to 0; in reality the flux saturates. Three saturation mechanisms are known. First, nonlocal electromagnetic response (spatial dispersion), where the polarization at a point depends on the field in a neighborhood, cuts off the divergence at roughly atomic scales. Second, phonon tunnelling: lattice vibrations on opposite sides of the gap couple through electrostatic and van der Waals interactions, so vibrational energy crosses the vacuum as if the gap were a weak elastic link; this was analyzed in a Landauer transmission picture by Chiloyan et al. for sub-nanometre gaps and by Pendry, Sasihithlu and Craster for vacuum-separated surfaces. Third, conduction-radiation coupling (CR coupling): the radiated power is large enough to establish temperature gradients inside the solids themselves, and the resulting internal temperature profiles feed back on the radiated flux. The source paper, Messina, Jin and Rodriguez, Phys. Rev. B 94, 121410(R) (2016), gave the first quantitative planar-geometry treatment of this third mechanism, showing with closed-form scattering-matrix expressions that the flux saturates toward the closed-gap conductive transfer rate at separations of tens of nanometres for materials of moderate thermal conductivity such as silica, and noting that at atomistic scales where continuum electrodynamics fails, the boundary between phonon-mediated and radiative conduction is blurred. Experiments have mapped the edges of this problem: FE was verified to be quantitatively accurate down to gaps of about 2 nanometres for doped silicon by Kim et al. (Nature 528, 387 (2015)), but below roughly 10 nanometres (the so-called extreme near field) the record is contradictory - Kloppstech et al. measured gold tip-plane fluxes four orders of magnitude above FE predictions, while Cui et al., after aggressive surface cleaning under ultra-high vacuum, found conductances below their detection limit; Rincón-García et al. confirmed FE for planar platinum and gold down to small gaps, and a 2025 measurement by Geesmann et al. kept the debate explicitly open. A 2025 study by López-Nebreda et al. traced anomalous thermal signals in metallic nanogaps to water menisci, showing that contamination can masquerade as exotic transport. On the theory side, atomistic tools exist for each channel separately: molecular dynamics (MD, atom-by-atom simulation of the lattice dynamics) combined with the phonon nonequilibrium Green's function (NEGF) method (a scattering formalism for vibrational transmission, in the same spirit as electronic Landauer transport) quantifies phonon tunnelling; FE quantifies the photonic channel; electron-tunnelling heat transfer has its own treatments. What does not exist is a single consistent microscopic theory that treats the radiative, phononic, and electronic channels on an equal footing across the crossover and locates, as a function of gap, material, and temperature, where near-field radiation hands over to near-contact (tunnelling-mediated) conduction - the issue the source paper flagged and the Reviews of Modern Physics (2021) outlook still lists as an unmet challenge requiring carriers to be treated on equal footing.

Problem Statement

Construct a consistent microscopic theory of heat transfer between two solid objects separated by a vacuum gap that spans the crossover from the near-field radiative regime, where continuum fluctuational electrodynamics (the Rytov theory of heat radiation from thermally fluctuating microscopic currents in matter) with local dielectric response is valid, down to atomic and sub-nanometre separations, where continuum electrodynamics and Fourier conduction (the standard diffusive law of heat conduction) both fail and the boundary between radiative and phonon-mediated (and, in metals, electron-mediated) transfer is blurred. The theory must treat the electromagnetic (photonic), phononic, and electronic energy-transfer channels on an equal, unified footing, determining whether and where their cross-channel coupling is essential and where an independent-channel (summed-conductance) description suffices, and must yield quantitative, channel-resolved predictions for the heat flux or thermal conductance as a function of gap size, material, and temperature, including whether and where near-field radiative transfer gives way to tunnelling-mediated near-contact conduction. The theory must also capture, within one formulation, radiation-induced internal temperature gradients, flux saturation, and - under large gradients - the feedback of the induced nonuniform temperatures on the material transport coefficients, and must agree with the existing experimental record, including the discrimination of genuine transport mechanisms from contamination and water-meniscus artifacts.

References

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