It has been shown recently that the Coulomb part of electromagnetic interactions is more important than the transverse propagation waves for the near-field enhancement of heat transfer between metal objects at a distance of order nanometers. Here we present a theory focusing solely on the Coulomb potential between electrons hopping among tight-binding sites. When the relevant systems are reduced to very small geometry, for example, a single site, the enhancement is much higher compared to a collection of them packed within a distance of a few Å. We credit this to the screening effect. This result may be useful in designing metal-based metamaterials to enhance heat transfer much higher.
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