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We introduce a novel type of self-bound droplet which carries an emergentcolor charge. We consider a system of particles hopping on a lattice andinteracting via a commensurately sign-changing potential which is attractive ata short range. The droplet formation is heralded by spontaneous crystallizationinto topologically distinct domains. This endows each droplet with an emergentcolor charge governing their mutual interactions: attractive for equal colorsand repulsive otherwise. The number of allowed colors is fixed only by thediscrete spatial symmetries of the sign-changing part of the interactionpotential. With increasing interaction range, the droplets become progressivelymore mobile, with their color charge still being energetically protected,allowing for nontrivial viscous dynamics of the interacting droplet plasmasformed during cooling. Sign-changing potentials with a short-range attractionappear quite naturally for light-mediated interactions and we concretelypropose a realization in state-of-the-art experiments with cold atoms in amultimode optical cavity.

Crystalline droplets with emergent topological color-charge in many-body systems with sign-changing interactions