Topology in Thermal, Particle, and Plasma Diffusion Metamaterials.

Diffusion is a fundamental process in the transfer of mass and energy. Diffusion metamaterials, a class of engineered materials with distinctive properties, enable precise control and manipulation of diffusion processes. Meanwhile, topology, a branch of mathematics, has attracted growing interest within the condensed matter physics community. Recently, the integration of diffusion metamaterials and topology has established a groundbreaking framework for understanding and controlling mass and energy transport processes. This review examines the rapidly emerging field of topological diffusion metamaterials, emphasizing how topological principles enhance robustness and precision in diffusion-driven systems, including thermal, particle, and plasma transport. The foundational theories of this field integrate basic topological theories from topological physics with the core theories of diffusion metamaterials, encompassing transformation theory and its various extensions. Additional related topics, beyond metamaterials, are also discussed. These advancements may have significant applications in various disciplines, including chemistry, enabling unprecedented levels of control in areas such as microfluidic heat management, targeted drug delivery, plasma etching, and beyond.