Effect of an electric field in the heat transfer between metals in the extreme near field

Radiative heat transfer between metals in the extreme near field in the presence of a potential difference between them has been calculated. Because of the coupling between the electric field of radiation and displacements of the surfaces, the radiative heat flux between two gold plates at nanometer distances that is due to $p$-polarized electromagnetic waves increases by many orders of magnitude at the variation of the potential difference from 0 to 10 V. The radiative mechanism of heat transfer is compared to the phonon mechanism associated with the electrostatic and van der Waals interactions. The phonon mechanism determined by the van der Waals interaction dominates at subnanometer distances and small potential difference. However, the radiative contribution dominates at nanometer distances because the phonon contribution decreases with increasing distance more rapidly than the radiative contribution. The results obtained in this work can be used to control heat fluxes at a nanoscale by means of the potential difference.