Diffusion metamaterials

Diffusion and wave propagation are both fundamental transport mechanisms, but they have intrinsically different dynamics, governing equations, and applications. Over the past decade, studies have emerged that use the transformation principle and metamaterials to control diffusion. Such research has led to new discoveries and exciting applications for manipulating the transport of mass (for example, particles and plasmas) and energy (such as heat). This Review introduces the basic principles, materials advances and applications of metamaterials that modulate the diffusion of heat, particles and plasmas. The theory begins with the application of the transformation principle to the diffusion equations. This approach is then generalized to incorporate non-Hermiticity, topology, non-reciprocity and spatiotemporal modulation, thus going beyond the conventional scope of metamaterials. Finally, we analyse the primary challenges associated with the design and fabrication of diffusion metamaterials and suggest several future directions, such as research into topological diffusion and machine-learning-assisted materials design.