  Very recently it has been predicted that the far-field radiative heat
transfer between two macroscopic systems can largely overcome the limit set by
Planck's law if one of their dimensions becomes much smaller than the thermal
wavelength ($\lambda_{\rm Th} \approx 10\, \mu$m at room temperature). To
explore the ultimate limit of the far-field violation of Planck's law, here we
present a theoretical study of the radiative heat transfer between
two-dimensional (2D) materials. We show that the far-field thermal radiation
exchanged by two coplanar systems with a one-atom-thick geometrical cross
section can be more than 7 orders of magnitude larger than the theoretical
limit set by Planck's law for blackbodies and can be comparable to the heat
transfer of two parallel sheets at the same distance. In particular, we
illustrate this phenomenon with different materials such as graphene, where the
radiation can also be tuned by a external gate, and single-layer black
phosphorus. In both cases the far-field radiative heat transfer is dominated by
TE-polarized guiding modes and surface plasmons play no role. Our predictions
provide a new insight into the thermal radiation exchange mechanisms between 2D
materials.
