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 $z_h\approx 0.5$, a roughness exponent ${\alpha }_h\approx 0.9$ and a super–ballistic growth exponent ${\beta }_h\approx 1.7$. 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 towards a unique non–equilibrium universality class associated with self–propelled interfaces of non–standard shape.