Shape-specific fluctuations of an active colloidal interface

Motivated by a recently synthesizable class of active interfaces formed by linked self-propelled colloids, we investigate the dynamics and fluctuations of a phoretically (chemically) interacting active interface with roto-translational coupling. We enumerate all steady-state shapes of the interface across parameter space and identify a regime where the interface acquires a finite curvature, leading to a characteristic "C-shaped" topology, along with persistent self-propulsion. In this phase, the interface height fluctuations obey Family-Vicsek scaling but with novel exponents: a dynamic exponent zh ≈ 0.5, a roughness exponent αh ≈ 0.9, and a super-ballistic growth exponent βh ≈ 1.7. In contrast, the orientational fluctuations of the colloidal monomers exhibit a negative roughness exponent, reflecting a surprising smoothness law, where steady-state fluctuations diminish with increasing system size. Together, these findings point toward a unique non-equilibrium universality class associated with self-propelled interfaces of non-standard shape.