  It has been shown recently that the Coulomb part of electromagnetic
interactions is more important than 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 angstroms. We credit this to the screening effect.
This result may be useful in designing metal-based meta-materials to enhance
heat transfer much higher.
