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

Exploring the limits of super-Planckian far-field radiative heat transfer using 2D materials