  The timescale of electronic cooling is an important parameter controlling the
performance of devices based on quantum materials for optoelectronic,
thermoelectric and thermal management applications. In most conventional
materials, cooling proceeds via the emission of phonons, a relatively slow
process that can bottleneck the carrier relaxation dynamics, thus degrading the
device performance. Here we present the theory of near-field radiative heat
transfer, that occurs when a two-dimensional electron system is coupled via the
non-retarded Coulomb interaction to a three-dimensional bulk that can behave as
a very efficient electronic heat sink. We apply our theory to study the cooling
dynamics of surface states of three dimensional topological insulators, and of
graphene in proximity to small-gap bulk materials. The ``Coulomb cooling'' we
introduce is alternative to the conventional phonon-mediated cooling, can be
very efficient and dominate the cooling dynamics under certain circumstances.
We show that this cooling mechanism can lead to a sub-picosecond time scale,
significantly faster than the cooling dynamics normally observed in Dirac
materials.
