We show that periodic multilayered structures allow to drastically enhance near-field radiative heat transfer between nanoparticles. In particular, when the two nanoparticles are placed on each side of the multilayered structure, at the same interparticle distance the resulting heat transfer is more than five orders of magnitude higher than that in the absence of the multilayered structure. This enhancement takes place in a broad range of distances and is due to the fact that the intermediate multilayered structure supports hyperbolic phonon polaritons with the key feature that the edge frequencies of the Type I and Type II Reststrahlen bands coincide with each other at a value extremely close to the particle resonance. This allow a very high-k evanescent modes resonating with the nanoparticles. Our predictions can be relevant for effective managing of energy at the nano-scale.
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