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.