Tunneling of heat between metals

We provide a theory of how heat tunnels between two parallel metal surfaces separated by an air gap. Two contributions are calculated: (1) electron-electron interactions and (2) photon fields from surface plasmons. Both contributions can transfer energy through low energy electron pairs. Our concern is with heat flow for small air gaps, on the order of nanometers. In that case the contribution from electron-electron interactions is most important. The contribution from photons is more important at larger separations.

Figure 1

Diagram for correlation energy and surface plasmon interactions.

Figure 2

Integration limits for $\int dudv$ are the diamond-shaped area. The vertical dashed line is at $u_0$.