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It is well established that near-field radiative heat transfer (NFRHT) canexceed Planck's blackbody limit1 by orders of magnitude owing to the tunnelingof evanescent electromagnetic frustrated and surface modes2-4, as has beendemonstrated experimentally for NFRHT between two large parallel surfaces5-7and between two subwavelength membranes8,9. However, while nanostructures canalso sustain a much richer variety of localized electromagnetic modes at theircorners and edges,10,11 the contributions of such additional modes to furtherenhancing NFRHT remain unexplored. Here, for the first time, we demonstrateboth theoretically and experimentally a new physical mechanism of NFRHTmediated by these corner and edge modes, and show it can dominate the NFRHT inthe "dual nanoscale regime" in which both the thickness of the emitter andreceiver, and their gap spacing, are much smaller than the thermal photonwavelengths. For two coplanar 20 nm thick SiC membranes separated by a 100 nmvacuum gap, the NFRHT coefficient at room temperature is both predicted andmeasured to be 830 W/m2K, which is 5.5 times larger than that for two infiniteSiC surfaces separated by the same gap, and 1400 times larger than thecorresponding blackbody limit accounting for the geometric view factor betweenthe emitter and receiver. This enhancement is dominated by the electromagneticcorner and edge modes which account for 81% of the NFRHT between these SiCmembranes. These findings are important for future NFRHT applications inthermal management and energy conversion.

Large enhancement of near-field radiative heat transfer in the dual nanoscale regime enabled by electromagnetic corner and edge modes