  Using the nonequilibrium Green's function formalism, we propose a general
microscopic framework to investigate the radiative heat transfer (RHT) between
coplanar objects with a square lattice. We employ the obtained formulas to
two-dimensional (2D) metal configurations with a tight-binding model and the
Drude model. Our results reveal that the RHT between coplanar 2D metals is
significantly larger than black-body radiation in both the near and far fields,
leading to a global super-Planckian RHT. As the separation distance increases,
the heat flux density exhibits a rapid decrease in the near field, followed by
a slower decrease and eventual $1/d$ dependence in the far field, while
maintaining a much higher magnitude than black-body radiation. Evanescent waves
dominate the heat transfer in the near field, while propagating waves dominate
the far field. Surprisingly, the propagating heat flux remains almost constant
over a wide range of distances, resulting in a super-Planckian behavior in the
far field. The dispersion relation of the spectrum function reveals distinct
contributions from propagating and evanescent waves, with possible origins from
surface plasmon resonance. These findings provide insights into the unique
characteristics of RHT between coplanar 2D metals and highlight the potential
for achieving enhanced heat transfer beyond the black-body limit. Our method is
applicable to any coplanar objects with square lattices, paves the way for
expanded investigations into various lattice geometries.
