Recent experimental measurements for near-field radiative heat transfer between two bodies have been able to approach the gap distance within $2\mathrm{nm}$, where the contributions of Coulomb fluctuation and electron tunneling are comparable. Using the nonequilibrium Green's function method in the $G_0{W}_0$ approximation, based on a tight-binding model, we obtain for the energy current a Caroli formula from the Meir-Wingreen formula in the local equilibrium approximation. Also, the Caroli formula is consistent with the evanescent part of the heat transfer from the theory of fluctuational electrodynamics. We go beyond the local equilibrium approximation to study the energy transfer in the crossover region from electron tunneling to Coulomb fluctuation based on a numerical calculation.

• Received 25 January 2018
• Revised 17 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.195450