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  • Review Article
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Diffusion metamaterials

Nature Reviews Physics volume 5, pages 218–235 (2023)Cite this article

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Abstract

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.

Key points

  • Metamaterials can control the diffusion of heat, particles and plasma to enable the cloaking, rotating or converging of the respective fields.

  • The transformation principle can be used to control processes with governing equations that are form-invariant under coordinate transformations, enabling the control of diffusion processes by changing material parameters such as conductivity.

  • The unique properties of diffusion metamaterials make them useful tools for studying new physical concepts such as non-Hermitian topology, non-reciprocity and spatiotemporal modulation.

  • Some potential engineering applications of these devices include thermal camouflage, heat harvesting, particle separation and plasma-based wound healing.

  • Future work in the field of diffusion metamaterials may include the development of devices to control topological diffusion or the use of machine learning to help with the design of new metamaterials.

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Fig. 1: Thermal metamaterials for manipulating heat conduction.
Fig. 2: Thermal metamaterials for manipulating heat conduction and convection.
Fig. 3: Topology and non-Hermitian physics in thermal metamaterials.
Fig. 4: Metamaterials for manipulating heat conduction, convection and radiation.
Fig. 5: Transformation diffusion and metamaterials.
Fig. 6: Manipulating particle diffusion with metamaterials.
Fig. 7: Plasma transport and metamaterials.

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Acknowledgements

We acknowledge financial support from the National Natural Science Foundation of China under grants no. 11725521, 12035004 and 12125504 and from the Science and Technology Commission of Shanghai Municipality under grant no. 20JC1414700.

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  1. These authors contributed equally: Zeren Zhang, Liujun Xu.

Authors and Affiliations

  1. Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai, China

    Zeren Zhang, Teng Qu, Min Lei & Jiping Huang

  2. Graduate School of China Academy of Engineering Physics, Beijing, China

    Liujun Xu

  3. School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China

    Zhi-Kang Lin & Jian-Hua Jiang

  4. School of Materials Science and Engineering, Xiangtan University, Xiangtan, China

    Xiaoping Ouyang

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Z.Z. researched data for the article. Z.Z., L.X., J.-H.J. and J.H. contributed substantially to discussion of the content. All authors wrote the article. J.-H.J. and J.H. reviewed and/or edited the manuscript before submission.

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Glossary

Bulk–edge correspondence

A topological phenomenon that means that the topological properties of the bulk of the system determine the character of the edge modes.

Concentrator

A structure that creates a larger flow (for example, heat flow) inside a device without disturbing the external fields (for example, temperature distribution) in the surrounding area.

Cloak

A structure that provides a zero gradient (for example, temperature gradient) inside a device without disturbing the external fields (for example, temperature distribution) in the surrounding area.

Darcy’s law

An equation to describe slow and viscous fluid flow. This equation is usually applied to describe fluids in porous media.

Diffusive Fizeau drag

The observation that wavelike temperature fields propagate at different speeds in opposite directions when an orthogonal advection is applied. It is analogous to the Fizeau drag observed in electromagnetic fields moving through flowing water.

Geometric phase

The phase difference obtained when a system completes one cycle of an adiabatic process, which is caused by the geometrical properties of the Hamiltonian parameter space.

Reynolds number

A dimensionless quantity that is used to classify the flow type as laminar (values less than 1) or turbulent (values more than 1).

Rotator

A structure that changes the transport direction of the flow (for example, heat flow) inside a device without disturbing the external fields (for example, temperature distribution) in the surrounding area.

Scattering cancellation

An approach that designs coatings that can be applied to objects to cancel the scattering, making the object invisible to observers.

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Zhang, Z., Xu, L., Qu, T. et al. Diffusion metamaterials. Nat Rev Phys 5, 218–235 (2023). https://doi.org/10.1038/s42254-023-00565-4

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