  Quantum emitters interacting with two-dimensional photonic-crystal baths
experience strong and anisotropic collective dissipation when they are
spectrally tuned to 2D Van-Hove singularities. In this work, we show how to
turn this dissipation into coherent dipole-dipole interactions with tuneable
range by breaking the lattice degeneracy at the Van-Hove point with a
superlattice geometry. Using a coupled-mode description, we show that the
origin of these interactions stems from the emergence of a qubit-photon bound
state which inherits the anisotropic properties of the original dissipation,
and whose spatial decay can be tuned via the superlattice parameters or the
detuning of the optical transition respect to the band-edges. Within that
picture, we also calculate the emitter induced dynamics in an exact manner,
bounding the parameter regimes where the dynamics lies within a Markovian
description. As an application, we develop a four-qubit entanglement protocol
exploiting the shape of the interactions. Finally, we provide a
proof-of-principle example of a photonic crystal where such interactions can be
obtained.
