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Diffusion metamaterials with artificial spatial structures have significant potential in controlling energy and mass transfer. Those static structures may lead to functionality and tunability constraints, impeding the application scope of diffusion metamaterials. Dynamic structures, adding the temporal dimension, have recently provided a new possibility for electric charge and heat diffusion regulation. This perspective introduces the fundamental theories and practical constructions of spatiotemporal diffusion metamaterials for achieving nonreciprocal, topological, or tunable properties. Compared with traditional static design, spatiotemporal modulation is promising to manipulate diffusion processes dynamically, with applications of real-time thermal coding and programming. Existing spatiotemporal diffusion explorations are primarily at macroscopic systems, and we may envision extending these results to microscale and other physical domains like thermal radiation and mass diffusion shortly., Comment: 5 pages, 3 figures. A perspective accepted by APL in press

Thermal nonreciprocity plays a vital role in chip heat dissipation, energy-saving design, and high-temperature hyperthermia, typically realized through the use of advanced metamaterials with nonlinear, advective, spatiotemporal, or gradient properties. However, challenges such as fixed structural designs with limited adjustability, high energy consumption, and a narrow operational temperature range remain prevalent. Here, a systematic framework is introduced to achieve reconfigurable, zero-energy, and wide-temperature thermal nonreciprocity by transforming wasteful heat loss into a valuable regulatory tool. Vertical slabs composed of natural bulk materials enable asymmetric heat loss through natural convection, disrupting the inversion symmetry of thermal conduction. The reconfigurability of this system stems from the ability to modify heat loss by adjusting thermal conductivity, size, placement, and quantity of the slabs. Moreover, this structure allows for precise control of zero-energy thermal nonreciprocity across a broad temperature spectrum, utilizing solely environmental temperature gradients without additional energy consumption. This research presents a different approach to achieving nonreciprocity, broadening the potential for nonreciprocal devices such as thermal diodes and topological edge states, and inspiring further exploration of nonreciprocity in other loss-based systems., Comment: 23 pages, 4 figures

Geometric phases in particle diffusion systems, an intriguing aspect enlightened from thermal systems, offer a different understanding beyond traditional Brownian motion and Fick's laws. This concept introduces a phase factor with significant implications for particle behavior, central to which is the non-Hermitian nature of the Hamiltonian in the diffusion system. A unique structure composed of two rings moving in opposite directions and a stationary intermediate layer plays multifunctional roles in controlling particle diffusion. For the real-world application, a bilayer particle-diffusion cloak is demonstrated, showcasing the extensive control and adaptability achievable through mastering geometric phases. This system has potential applications in industries like healthcare and environmental management, thus expanding the understanding of the geometric phase and offering insights for the design of particle-diffusion metamaterials., Comment: 14 pages, 4 figures. This review article explores the Non Hermitian topological theory in regulating particle diffusion, a concept prominently evidenced by the landmark thermal study Anti parity time Symmetry in Diffusive Systems published in Science, 2019. The review is slated for publication in the forthcoming book, Diffusionics, Diffusion Processes Governed by Diffusion Metamaterials

Thermal metamaterials have made significant advancements in the past few decades. However, the concept of thermal metamaterials is primarily rooted in the thermal conduction mechanism, which has consequently restricted their application scope. It is imperative to consider thermal radiation, another crucial thermal transport mechanism, particularly in high-temperature regimes, when designing thermal devices. In this review paper, we present the advancements in this area, with a specific focus on research conducted using the effective-medium theory. Additionally, we explore the potential applications of radiative thermal metamaterials and discuss prospective research directions from a microscopic perspective for future investigations.

Heat flux rotation has important significance in thermal protection since it can shield the heat energy from a selected direction. Combining with tailored metamaterials, transformation thermotics provides a powerful way to manipulate heat flux, and various kinds of thermal meta-devices have been designed including thermal rotator. However, the existing transformation-thermotics-based thermal rotator can only work in a fixed background. Remanufacturing is inevitable when background changes, which is inconvenient and restricts the practical application. Here, we propose a novel mechanism for chameleonlike thermal rotator. The designed rotator can adaptively change its thermal conductivity with the object nearby while rotating heat flux without distorting the background temperature profile, just like a chameleon in nature. Moreover, such rotator is made of transformation-invariant material, thus its constitutive parameters do not change under arbitrary coordinate transformations. Therefore, the proposed rotator also has functionality-invariance beyond shape adjustment, and can theoretically transfer heat flux in arbitrary direction using different shapes of the same material. A prototype rotator was designed and fabricated, and its chameleonlike behavior is successfully demonstrated. Our concept provides a guidance to design chameleonlike thermal meta-devices and can be extended to other fields like acoustics, hydrodynamics, etc. The chameleonlike thermal rotator will have potential applications for the implementation of adaptive and adjustable metamaterials., Comment: This article has been accepted by International Conference on Thermodynamics and Thermal Metamaterials (ThermoMeta) as Proceedings of ThermoMeta, 1, 10001 (2020)

Thermal metamaterial represents a groundbreaking approach to control heat conduction, and, as a crucial component, thermal invisibility is of utmost importance for heat management. Despite the flourishing development of thermal invisibility schemes, they still face two limitations in practical applications. First, objects are typically completely enclosed in traditional cloaks, making them difficult to use and unsuitable for objects with heat sources. Second, although some theoretical proposals have been put forth to change the thermal conductivity of materials to achieve dynamic invisibility, their designs are complex and rigid, making them unsuitable for large-scale use in real three-dimensional spaces. Here, we propose a concept of a thermal dome to achieve three-dimensional invisibility. Our scheme includes an open functional area, greatly enhancing its usability and applicability. It features a reconfigurable structure, constructed with simple isotropic natural materials, making it suitable for dynamic requirements. The performance of our reconfigurable thermal dome has been confirmed through simulations and experiments, consistent with the theory. The introduction of this concept can greatly advance the development of thermal invisibility technology from theory to engineering and provide inspiration for other physical domains, such as direct current electric fields and magnetic fields.

Diffusion driven by temperature or concentration gradients is a fundamental mechanism of energy and mass transport, which inherently differs from wave propagation in both physical foundations and application prospects. Compared with conventional schemes, metamaterials provide an unprecedented potential for governing diffusion processes, based on emerging theories like the transformation and the scattering cancellation theory, which enormously expanded the original concepts and suggest innovative metamaterial-based devices. We hereby use the term "diffusionics" to generalize these remarkable achievements in various energy (e.g., heat) and mass (e.g., particles and plasmas) diffusion systems. For clarity, we categorize the numerous studies appeared during the last decade by diffusion field (i.e., heat, particles, and plasmas) and discuss them from three different perspectives: the theoretical perspective, to detail how the transformation principle is applied to each diffusion field; the application perspective, to introduce various intriguing metamaterial-based devices, such as cloaks and radiative coolers; and the physics perspective, to connect with concepts of recent concern, such as non-Hermitian topology, nonreciprocal transport, and spatiotemporal modulation. We also discuss the possibility of controlling diffusion processes beyond metamaterials. Finally, we point out several future directions for diffusion metamaterial research, including the integration with artificial intelligence and topology concepts., Comment: This review article has been published in Reviews of Modern Physics, volume 96, 015002 (2024)

Material science is an important foundation of modern society development, covering significant areas like chemosynthesis and metamaterials. Click chemistry provides a simple and efficient paradigm for achieving molecular diversity by incorporating modified building blocks into compounds. In contrast, most metamaterial designs are still case by case due to lacking a fundamental mechanism for achieving reconfigurable thermal conductivities, largely hindering design flexibility and functional diversity. Here, we propose a universal concept of click metamaterials for fast realizing various thermal conductivities and functionalities. Tunable hollow-filled unit cells are constructed to mimic the modified building blocks in click chemistry. Different hollow-filled arrays can generate convertible thermal conductivities from isotropy to anisotropy, allowing click metamaterials to exhibit adaptive thermal functionalities. The straightforward structures enable full-parameter regulation and simplify engineering preparation, making click metamaterials a promising candidate for practical use in other diffusion and wave systems., Comment: Here, click metamaterials have been proposed and swiftly generate variable thermal conductivities and functionalities by using tunable hollow-filled cells akin to the modified building blocks in click chemistry. This breakthrough holds the promise to transform applications in a range of diffusion and wave systems, thereby having a profound impact on the development of materials science

Emerging multiphysics metamaterials offer a distinct possibility for regulating complex physical processes. However, two severe constraints still lower their functionality and tunability. First, multiphysics functionality is fixed once structures and materials are prepared, i.e., one functionality for one physical field. Second, continuous tunability is unavailable in multiphysics fields because parameters are hard to change on demand. Here, we propose the concept of spatiotemporal multiphysics metamaterials by delicately considering the temporal dimension. The spatiotemporal feature leads to multiple functions for each physical field and their continuous switching. We achieve flexible thermal and electric function switching between cloaking, sensing, and concentrating based on rotatable checkerboard structures with different rotation times, material composition, and geometric shapes. Real-time thermal and electric functions are theoretically predicted and confirmed by simulations. These results provide a promising spatiotemporal platform for realizing adaptive and intelligent multiphysics field manipulation.

Heat management is crucial for state-of-the-art applications such as passive radiative cooling, thermally adjustable wearables, and camouflage systems. Their adaptive versions, to cater to varied requirements, lean on the potential of adaptive metamaterials. Existing efforts, however, feature with highly anisotropic parameters, narrow working-temperature ranges, and the need for manual intervention, which remain long-term and tricky obstacles for the most advanced self-adaptive metamaterials. To surmount these barriers, we introduce heat-enhanced thermal diffusion metamaterials powered by deep learning. Such active metamaterials can automatically sense ambient temperatures and swiftly, as well as continuously, adjust their thermal functions with a high degree of tunability. They maintain robust thermal performance even when external thermal fields change direction, and both simulations and experiments demonstrate exceptional results. Furthermore, we design two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response. This work offers a framework for the design of intelligent thermal diffusion metamaterials and can be expanded to other diffusion fields, adapting to increasingly complex and dynamic environments., Comment: This paper has been accepted for publication in Advanced Materials

Transformation media provide a fundamental paradigm for field regulation, but their tricky anisotropy challenges fabrication. Though optical conformal mapping has been utilized to eliminate anisotropy, two key factors still hinder its development in thermotics, i.e., the distinct diffusion nature and inevitable interface mismatching. Here, we put forth the concept of diffusive pseudo-conformal mapping, overcoming the inherent difference between diffusion and waves and achieving perfect interface matching. The proposed mapping directly leads to heat guiding and expanding functions with anisotropy-free transformation thermal media, whose feasibility is confirmed by experiments or simulations. Besides diverse applications, we provide a unified perspective for two distinct types of prevailing bilayer cloaks by uncovering their profound ties with pseudo-conformal mapping. These results greatly simplify the preparation of transformation thermotics and have implications for regulating other diffusion and wave phenomena.

Thermal metamaterials provide rich control of heat transport which is becoming the foundations of cutting-edge applications ranging from chip cooling to biomedical. However, due to the fundamental laws of physics, the manipulation of heat is much constrained in conventional thermal metamaterials where effective heat conduction with Onsager reciprocity dominates. Here, through the inclusion of thermal convection and breaking the Onsager reciprocity, we unveil a regime in thermal metamaterials and transformation thermotics that goes beyond effective heat conduction. By designing a liquid-solid hybrid thermal metamaterial, we demonstrate a continuous switch from thermal cloaking to thermal concentration in one device with external tuning. Underlying such a switch is a topology transition in the virtual space of the thermotic transformation which is achieved by tuning the liquid flow via external control. These discoveries illustrate the extraordinary heat transport in complex multi-component thermal metamaterials and pave the way toward an unprecedented regime of heat manipulation.

Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form similarity between Schrodinger equation and diffusion equation, researches on higher-order topological insulators have been extended from condensed matter physics to thermal diffusion. Unfortunately, all the corner states of thermal higher-order topological insulator reside within the band gap. Another kind of corner state, which is embedded in the bulk states, has not been realized in pure diffusion systems so far. Here, we construct higher-dimensional Su-Schrieffer-Heeger models based on sphere-rod structure to elucidate these corner states, which we term ``in-bulk corner states". Due to the anti-Hermitian properties of diffusive Hamiltonian, we investigate the thermal behaviour of these corner states through theoretical calculation, simulation, and experiment. Furthermore, we study the different thermal behaviours of in-bulk corner state and in-gap corner state. Our results would open a different gate for diffusive topological states and provide a distinct application for efficient heat dissipation.

Black holes are one of the most intriguing predictions of general relativity. So far, metadevices have enabled analogous black holes to trap light or sound in laboratory spacetime. However, trapping heat in a conductive ambient is still challenging because diffusive behaviors are directionless. Inspired by black holes, we construct graded heat-conduction metadevices to achieve thermal trapping, resorting to the imitated advection produced by graded thermal conductivities rather than the trivial solution of using insulation materials to confine thermal diffusion. We experimentally demonstrate thermal trapping for guiding hot spots to diffuse towards the center. Graded heat-conduction metadevices have advantages in energy-efficient thermal regulation because the imitated advection has a similar temperature field effect to the realistic advection that is usually driven by external energy sources. These results also provide insights into correlating transformation thermotics with other disciplines such as cosmology for emerging heat control schemes.