  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.
