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Electric field effect in heat transfer in 2D devices

We calculate heat transfer between a 2D sheet (e.g. graphene) and a dielectric in presence of a gate voltage. The gate potential induces surface charge densities on the sheet and dielectric, which results in electric field, which is coupled to the surface displacements and, as a consequence, resulting an additional contributions to the radiative heat transfer. The electrostatic and van der Waals interactions between the surface displacement result in the phonon heat transfer, which we calculate taking into account the nonlocality of these interactions. Numerical calculations are presented for heat transfer between graphene and a SiO$_2$ substrate.