Spontaneous unidirectional rotation of a symmetric gear driven by spherical active particles

Time reversal asymmetry and spatial anisotropy are considered two prerequisites for Brownian ratchet. An intriguing realization can be achieved by placing an asymmetric gear in the suspension of motile rod-like bacteria. Usually, alignment interactions caused by anisotropic collisions or hydrodynamics would boost the ratchet effect. Here, we are concerned with a perfectly isotropic system, i.e., symmetric gear immersed in a bath of spherical active Brownian particles. We find that, under certain conditions, kinetic symmetry-breaking arises spontaneously, i.e., the symmetric gear keeps rotating in one direction. Unexpectedly, such ratchet phenomenon does not rely on the direct many-particle interactions and moreover the introduction of alignment interaction would counterintuitively prevent it from happening! Further investigation reveals that such spontaneous symmetry-breaking phenomenon shares similarities with the equilibrium phase transition of the Ising model. Our results provide new insights and enhance our understanding of the fundamental aspects of active ratchet phenomena.