Collective topological active particles: Non-ergodic superdiffusion and ageing in complex environments

•The collective motion of topological active particles in complex environments is investigated.•Both the ergodic ballistic-diffusion and the non-ergodic superdiffusion are observed.•The misalignment between the active particles and obstacles gives rise to the anisotropy of the particle motion and is the main mechanism of observed behaviors. We investigate the collective motion of active particles in complex environments. Two types of topological neighborhood, k-nearest neighbors and Voronoi tessellation, are considered, for each active particle interacts with other active particles or obstacles. By virtue of numerical simulations, we demonstrate the superdiffusion, ergodicity breaking and ageing in this system. The misalignment between the active particles and obstacles gives rise to the anisotropy of motion of topological active particles, and is the main mechanism of observed behaviors. Our work merges the non-ergodicity and superdiffusion and sheds light on the topological interaction of active particles in complex environments.