Spontaneous symmetry-breaking of the active cluster drives the directed movement and self-sustained oscillation of symmetric rod-like passive particles

-axis in an active bath can keep long-lived directed movement at nearly constant speed due to the spontaneous symmetry breaking of the neighboring active particle cluster. If the passive particle is further confined by a harmonic potential, it may undergo self-sustained periodic oscillation for an appropriate length of the passive particle and self-propelled velocity of active particles. The restoring force from the harmonic potential will trigger the velocity jump-off and thus lead to self-sustained periodic oscillation. Remarkably, the relationship between the velocity of the passive particle and the external force shows that the effective viscosity of the active bath may become negative in some regime. Finally, we develop a minimum 1D theoretical model to further probe the mechanism underlying the directed movement and self-sustained oscillation of the passive particle. Our findings reveal the effect of the moving boundary on the active bath and demonstrate a novel method to extract practical mechanical work from the active bath to propel microdevices.