  We investigate a two-dimensional Bose-Einstein condensate that is optically
driven via a retro-reflecting mirror, forming a single optical feedback loop.
This induces a peculiar type of long-range atomic interaction with highly
oscillatory behavior, and we show here how the sign of the underlying
interaction potential can be controlled by additional optical elements and
external fields. This additional tunability enriches the behavior of the system
substantially, and gives rise to a surprising range of new ground states of the
condensate. In particular, we find the emergence of self-bound crystals of
quantum droplets with various lattice structures, from simple and familiar
triangular arrays to complex superlattice structures and crystals with entirely
broken rotational symmetry. This includes mesoscopic clusters composed of small
numbers of quantum droplets as well as extended crystalline structures.
Importantly, such ordered states are entirely self-bound and stable without any
external in-plane confinement, having no counterpart to other quantum-gas
settings with long-range atomic interactions.
