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