Geometric phase and bilayer cloak in macroscopic particle-diffusion systems.

Particle diffusion is a fundamental process in various systems, so its effective manipulation is crucially important. For this purpose, here we design a basic structure composed of two moving rings with equal-but-opposite velocities and a stationary intermediate layer, which can realize multiple functions to control particle diffusion. On the one hand, the intermediate layer allows particle exchange between the two moving rings, which gives birth to an exceptional point of velocity. As a result, a geometric phase appears for a loop evolution of velocity containing the exceptional point. On the other hand, the two moving rings also enhance the effective diffusivity of the intermediate layer, which helps design a bilayer particle-diffusion cloak. The present cloak only requires homogeneous parameters and simple structures, and meanwhile, its on and off can be flexibly controlled by velocity. These results broaden the scope of geometric phase and provide hints for designing particle-diffusion metamaterials.