Historical research guide · 0644 · 2021
Near-field radiative heat transfer in many-body systems
S.-A. Biehs · R. Messina · P. S. Venkataram · A. W. Rodriguez · J. C. Cuevas · P. Ben-Abdallah
In one minute
Six physicists in Oldenburg, Palaiseau, Princeton, Madrid and Sherbrooke review what happens to thermal radiation when objects are brought closer together than the wavelength of the heat they emit — about ten micrometres at room temperature. Planck’s law, derived with ray optics, simply stops applying. Evanescent waves that normally die at a surface can tunnel across the gap, and the heat flux climbs far above the black-body limit: for two silica plates a nanometre apart, by almost five orders of magnitude. The review’s own subject is what happens with more than two bodies, and the answer is that heat exchange stops being additive — bring up a third object and the flux between the first two changes. The authors build a Landauer-style transmission theory, the mathematics normally used for electrons in mesoscopic wires, extended to any number of terminals and to materials that do not obey reciprocity. Out of it come thermal transistors, a Hall effect for radiation, and heat currents that circulate at equilibrium.
Connection
Chapter 2 treats the vacuum gap as a structured thing rather than a nothing, and here is a gap carrying a heat flux the textbook theory of radiation says should not be there, computed with the same fluctuational electrodynamics that gives the Casimir force. Chapter 6 is about getting useful work out of fluctuating fields, and near-field radiative transfer is the corner of that programme that is already hardware — near-field thermophotovoltaics, and the thermotronic devices this review maps. Keep the accounting straight while reading it: these systems move heat between bodies at different temperatures, they do not make it.
From the source
Planck’s law is not a ceiling, it is a far-field approximation. It was derived using ray optics and fails once the separation is smaller than the thermal wavelength, about ten micrometres at room temperature, because in that regime evanescent waves — photon tunnelling — carry the heat and are not counted in Planck’s law at all. Polder and van Hove predicted this within fluctuational electrodynamics in the early 1970s; it was hinted at experimentally in the late 1960s and firmly confirmed from the 2000s onward across many laboratories. For two silica plates at a one-nanometre gap the heat flux is almost five orders of magnitude larger than the black-body limit.Section I, Introduction; Section II B, Metals vs. dielectrics; Figures 1 and 3
Radiative heat exchange between many bodies is not additive. The power flowing between two objects is changed by the presence of the others through multiple scattering, so an N-body system is not the sum of its pairs — the authors present their expression for the exchanged power as itself a proof and a quantitative evaluation of that non-additivity, in both the dipolar and the macroscopic formulations.Section III A 3, Non-additivity in many-dipole systems; Section III B 2, Non-additivity in many-body systems
The unifying formalism is a generalised Landauer theory. Extending the Polder and van Hove stochastic formalism to N bodies, and treating their mutual interactions through multiple scattering, gives a Landauer-like description in which heat carried by thermal photons is set by transmission coefficients between terminals — the same structure used for coherent electron transport in mesoscopic conductors, and valid for arbitrary reciprocal and non-reciprocal multi-terminal systems. The same framework then covers both steady-state transport and relaxation dynamics towards local and global equilibrium.Abstract; Section I, Introduction; Section III B 1, Scattering-matrix formalism
In non-reciprocal systems there is a persistent heat current at global thermal equilibrium. For three magneto-optical nanoparticles the transmission coefficient from body one to body two differs from that from two to one, so the clockwise and anticlockwise power flows around the ring are unequal even when all three sit at the same temperature. The net power on each body still vanishes, so the persistent current heats and cools nothing — the asymmetry of the transmission spectra and the equilibrium temperature set its size. Measuring it is still an open problem; a setup near a magneto-optical planar sample has been proposed.Section III D 5, Persistent heat flux, angular momentum, spin and heat current; Equations (132) and (133); Figure 41
Many-body near-field transfer makes devices that have no two-body analogue. The review maps the emerging field of thermotronics — manipulating heat flux in analogy with electric current in circuits — including a radiative thermal transistor built as a three-terminal system with a silica source, a vanadium dioxide gate and a silica drain, whose amplification factor is clearly larger than one in the phase-change temperature region of the gate — negative thermal resistance being the necessary condition for any amplification at all; a Hall effect for thermal radiation; and heat-flux rectification using non-reciprocal surface waves. The stated aim is active thermal management, wireless sensors that use heat as their primary energy source, and low-electricity information processing.Section I, Introduction; Section III C 5, Dynamical control; Figure 32; Sections III D 6 and III D 7; Section IV, Outlook
The many-body regime has not yet been measured. Recent experiments have tuned radiative heat transfer in many-body systems by moving nearby objects, but to the authors’ knowledge many-body systems have yet to be experimentally investigated in the purely near-field regime. The Outlook names the open ground: two-dimensional systems, where the scaling of radiative conductance with system size is unknown; dense systems where weak and strong localisation of thermal radiation remain unexplored; the sub-nanometre gaps where photons, phonons and electrons all contribute and recent experiments still conflict; spin and angular-momentum transport in N-body systems; and non-Hermitian topological states.Section I, Introduction, closing paragraphs; Section IV, Outlook and open questions
The way in
https://doi.org/10.1103/RevModPhys.93.025009How to cite it
S.-A. Biehs, R. Messina, P. S. Venkataram, A. W. Rodriguez, J. C. Cuevas, P. Ben-Abdallah (2021) Near-field radiative heat transfer in many-body systems doi:10.1103/RevModPhys.93.025009