  Dirac energy-dispersions are responsible of the extraordinary transport
properties of graphene. This motivated the quest for engineering such energy
dispersions also in photonics, where they have been predicted to lead to many
exciting phenomena. One paradigmatic example is the possibility of obtaining
power-law, decoherence-free, photon-mediated interactions between quantum
emitters when they interact with such photonic baths. This prediction, however,
has been obtained either by using toy-model baths, which neglect polarization
effects, or by restricting the emitter position to high-symmetry points of the
unit cell in the case of realistic structures. Here, we develop a
semi-analytical theory of dipole radiation near photonic Dirac points in
realistic structures that allows us to compute the effective photon-mediated
interactions along the whole unit cell. Using this theory, we are able to find
the positions that maximize the emitter interactions and their range, finding a
trade-off between them. Besides, using the polarization degree of freedom, we
also find positions where the nature of the collective interactions change from
being coherent to dissipative ones. Thus, our results significantly improve the
knowledge of Dirac light-matter interfaces, and can serve as a guidance for
future experimental designs.
