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Thermal transport is a fundamental mechanism of energy transfer process quite distinct from wave propagation phenomena. It can be manipulated well beyond the possibilities offered by natural materials with a new generation of artificial metamaterials: thermal metamaterials. Topological physics, a focal point in contemporary condensed matter physics, is closely intertwined with thermal metamaterials in recent years. Inspired by topological photonics and topological acoustics in wave metamaterials, a new research field emerged recently, which we dub `topological thermotics', which encompasses three primary branches: topological thermal conduction, convection, and radiation. For topological thermal conduction, we discuss recent advances in both 1D and higher-dimensional thermal topological phases. For topological thermal convection, we discuss the implementation of thermal exceptional points with their unique properties and non-Hermitian thermal topological states. Finally, we review the most recent demonstration of topological effects in the near-field and far-field radiation. Anticipating future developments, we conclude by discussing potential directions of topological thermotics, including the expansion into other diffusion processes such as particle dynamics and plasma physics, and the integration with machine learning techniques., Comment: This perpective summarizes the topological physics in thermal metamaterials and proposes a new research field, "topological thermotics"

Improving the heat transfer coefficient is crucial across various energy utilization processes for maintaining device safety and stability with high energy efficiency. However, in scenarios with limited heat capacity flow rates, increasing the thermal conductivity of encapsulated internal heat source (IHS) packaging can paradoxically impede heat transfer. Herein, we introduced a convective-meta thermal dispersion (CMTD) strategy applicable throughout the energy domain. By integrating low thermal conductivity materials into high thermal conductivity package structures, we disrupted tangential heat flow while preserving efficient radial heat transport. Through this approach, a notable reduction in tangential temperature within the fluid channel was achieved, effectively lowering the IHS temperature. Remarkably, this cooling mechanism does not need additional energy input, thermal property enhancements, or expanded heat transfer areas, which are often prerequisites in existing technologies. Moreover, spontaneous enhancement phenomena emerged under constrained heat transfer conditions, termed self-adaptive cooling enhancement. Our investigations revealed, under steady-state conditions, a maximum 24.5% decrease in IHS average temperature, while transient conditions exhibited a maximum 32.3% increase in heat transfer between the IHS and cooling fluid, validating the efficacy of the CMTD strategy. These findings offer a promising pathway for efficient thermal management in various thermal energy utilization fields with high power density such as nuclear fission and fusion and contributed to a deeper understanding of fundamental fluid-solid heat transfer mechanisms across the energy science.

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

Thermoelectric devices are pivotal in the energy sector, with enhancing their conversion efficiency being a longstanding focal point. While progress has been made, overcoming the inherent low efficiency and heat management issues remains challenging. The advent of thermal metamaterials, particularly thermal concentrators, holds promise for improved thermoelectric efficiency. The concentrator has the potential to amplify the temperature gradient within the working region without altering the temperature gradient of the background, thereby enhancing thermoelectric conversion efficiency through this concentrating effect. Nevertheless, the efficacy of this effect is contingent upon the structural parameters of the concentrator. Systematically investigating the impact of metamaterials on thermoelectric conversion efficiency, particularly in terms of quantifying the enhancement, presents a significant challenge. Additionally, the intrinsic thermal conductivity of the material imposes constraints on the applicability of the concentrator in this regard. In this context, drawing inspiration from the recently proposed passive ultra-conductive heat transport scheme, we have devised expanded-plane bilayer thermal concentrators. We substantiate the prospective performance of our design through analytical demonstration, further validated through finite-element simulations and experiments. Notably, through direct calculation, we illustrate an efficiency improvement of about 38\% when utilizing the expanded-plane concentrator comparing with not using expanded-plane structure. The expanded-plane geometrical configuration of the outer layer can also attain large-scale value. These findings not only present a novel avenue for the functional transformation of thermal metamaterials but also hold significant implications for the field of thermoelectrics.

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

Active metadevices with external excitations exhibit significant potential for advanced heat regulation. Nonetheless, conventional inputs, like heating/cooling and introducing convection by rotating plate, display inherent limitations. One is the only focus on far-field control to eliminate temperature distortion in the background while neglecting near-field regulation in the functional region. Another is lacking adaptability due to complex devices like thermoelectric modules and stepping motors. To tackle these challenges, the concept of diffusive superimposed dipoles characterized by orthogonal thermal dipole moments is proposed. Cooperative near- and far-field regulation of temperature fields is achieved by designing superimposed dipole moments, enabling transparency and cloaking functionalities. Simulation and experiment outcomes affirm the efficacy of this adaptive thermal field control technique, even when interface thermal resistance is taken into account. Adaptivity stems from dipole moment decomposability, allowing metadevices to operate in various heat flux directions and background thermal conductivity. These findings could pave the way for cooperative and adaptive thermal management and hold potential applications in other Laplace fields, including direct current and hydrodynamics., Comment: 12 pages, 11 figures

Thermal conduction force plays a crucial role in manipulating the local thermal conductivity of crystals. However, due to the diffusive nature of thermal conduction, investigating the force effect is challenging. Recently, researchers have explored the force effect based on the wave-like behavior of thermal conduction, specifically second sound. However, their focus has been primarily on the progressive case, neglecting the more complex standing temperature field case. Additionally, establishing a connection between the results obtained from the progressive case and the standing case poses a challenging problem. In this study, we investigate the force effect of standing and quasi-standing temperature fields, revealing distinct characteristics of thermal conduction force. Moreover, we establish a link between the progressive and standing cases through the quasi-standing case. Our findings pave the way for research in more intricate scenarios and provide an additional degree of freedom for manipulating the local thermal conductivity of dielectric crystals.

The precise measurement of temperature is crucial in various fields such as biology, medicine, industrial automation, energy management, and daily life applications. While in most scenarios, sensors with a fixed thermal conductivity inevitably mismatch the analogous parameter of the medium being measured, thus causing the distortion and inaccurate detection of original temperature fields. Despite recent efforts on addressing the parameter-mismatch issue, all current solutions are constrained to a fixed working medium whereas a more universal sensor should function in a variety of scenes. Here, we report a dynamic thermal sensor capable of highly accurate measurements in diverse working environments. Remarkably, thanks to the highly tunable thermal conductivity of the expanded-plane structure, this sensor works effect on background mediums with a wide range of conductivity. Such a development greatly enhances the robustness and adaptability of thermal sensors, setting a solid foundation for applications in multi-physical sensing scenarios.

Recent studies have identified plasma as a topological material. Yet, these researches often depict plasma as a fluid governed by electromagnetic fields, i.e., a classical wave system. Indeed, plasma transport can be characterized by a unique diffusion process distinguished by its collective behaviors. In this work, we adopt a simplified diffusion-migration method to elucidate the topological plasma transport. Drawing parallels to the thermal conduction-convection system, we introduce a double ring model to investigate the plasma density behaviors in the anti-parity-time reversal (APT) unbroken and broken phases. Subsequently, by augmenting the number of rings, we have established a coupled ring chain structure. This structure serves as a medium for realizing the APT symmetric one-dimensional (1D) reciprocal model, representing the simplest tight-binding model with a trivial topology. To develop a model featuring topological properties, we should modify the APT symmetric 1D reciprocal model from the following two aspects: hopping amplitude and onsite potential. From the hopping amplitude, we incorporate the non-reciprocity to facilitate the non-Hermitian skin effect, an intrinsic non-Hermitian topology. Meanwhile, from the onsite potential, the quasiperiodic modulation has been adopted onto the APT symmetric 1D reciprocal model. This APT symmetric 1D Aubry-Andr\'e-Harper model is of topological nature. Additionally, we suggest the potential applications for these diffusive plasma topological states. This study establishes a diffusion-based approach to realizing topological states in plasma, potentially inspiring further advancements in plasma physics., Comment: This letter has been published on Chinese Physics Letters as an express letter.Comments are welcome!

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

The Stirling engine, which possesses external combustion characteristics, a simple structure, and high theoretical thermal efficiency, has excellent potential for utilizing finite waste heat and cold resources. However, practical applications of this technology suffered from thermal inefficiency due to the discontinuity and instability of waste resources. Despite advances in energy storage technology, temperature variations in the heat-exchanging fluids at the hot and cold ends of the Stirling engine remained significant obstacles. In this work, convective meta-thermal concentration (CMTC) was introduced between the heating (cooling) fluids and the hot (cold) end of the Stirling engine, employing alternating isotropic materials with high and low thermal conductivities. It was demonstrated that CMTC effectively enhanced the temperature difference between the hot and cold ends, leading to a remarkable improvement in Stirling engine efficiency. Particularly, when the Stirling engine efficiency tended to zero due to the limited availability of waste heat and cold resources, CMTC overcame this limitation, surpassing existing optimization technology. Further analysis under various operating conditions showed that CMTC achieved a significant thermal efficiency improvement of up to 1460%. This work expanded the application of thermal metamaterials to heat engine systems, offering an exciting avenue for sustainable energy utilization.

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 to periodic systems, quasicrystals without translational invariance exhibit unexpected localization properties. The extended-localized transition in quasicrystals has been observed in both quantum and classical wave systems. However, its manifestation in diffusion systems, which serve as novel platforms for exploring phases of matter in condensed matter physics, remains unexplored. Here, we present the implementation of the extended-localized transition in a diffusive quasicrystal based on the coupled ring chain structure. By modulating the thermal conductivities of rings, we obtain the diffusive one-dimensional Aubry-Andr\'e-Harper (AAH) model, which exhibits an extended-localized transition. Thanks to the ring-shaped chain, we clearly demonstrate the extended-localized transition under the uniform excitation through temperature field simulations. For the localized state, the temperature field clearly demonstrates a multiple localization centers phenomenon, which has no counterpart in wave systems. We also quantitatively investigate the temperature evolution and size effect of this transition. Furthermore, the local excitation has been adopted to demonstrate the temperature field for both the extended and localized states. Besides, we implement the non-Hermitian diffusive AAH model by rotating rings, whose temperature field shows a moving multiple localization centers phenomenon in the localized phase. Finally, we give the experimental suggestions for the diffusive AAH model and propose a potential application named as double-trace distributed generator. Our results can facilitate the design of flexible thermal devices and efficient heat management.

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.

Using the extensively studied V2O3 as a prototype system, we investigate the role of percolation in metal-insulator transition (MIT). We apply scanning microwave impedance microscopy to directly determine the metallic phase fraction p and relate it to the macroscopic conductance G, which shows a sudden jump when p reaches the percolation threshold. Interestingly, the conductance G exhibits a hysteretic behavior against p, suggesting two different percolating processes upon cooling and warming. Based on our image analysis and model simulation, we ascribe such hysteretic behavior to different domain nucleation and growth processes between cooling and warming, which is likely caused by the decoupled structural and electronic transitions in V2O3 during MIT. Our work provides a microscopic view of how the interplay of structural and electronic degrees of freedom affects MIT in strongly correlated systems.

Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has never been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop, for the first time, a general theory of transformation thermal convection by considering the convection-diffusion equation, the Navier-Stokes equation, and the Darcy law. By introducing porous media, we get a set of coupled equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite element simulations confirm the theoretical findings. This work offers a general transformation theory for thermal convection, thus revealing some novel behaviors of thermal convection; it not only provides new hints on how to control heat transfer by combining thermal conduction, thermal radiation, and thermal convection, but also benefits the study of mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time., Comment: 17 pages, 6 figures

How to macroscopically control the flow of heat at will is up to now a challenge, which, however, is very important for human life since heat flow is a ubiquitous phenomenon in nature. Inspired by intelligent electronic components or intelligent materials, here we demonstrate, analytically and numerically, a unique class of intelligent bifunctional thermal metamaterials called thermal cloak-concentrators, which can automatically change from a cloak (concentrator) to a concentrator (cloak) when the applied temperature field decreases (increases). For future experimental realization, the behavior is also confirmed by assembling homogeneous isotropic materials according to the effective medium theory. The underlying mechanism originates from the effect of nonlinearity in thermal conduction. This work not only makes it possible to achieve a switchable Seebeck effect, but also offers guidance both for macroscopic manipulation of heat flow at will and for the design of similar intelligent multifunctional metamaterials in optics, electromagnetics, acoustics, or elastodynamics., Comment: 14 pages, 3 figures

The macroscopic control of ubiquitous heat flow remains poorly explored due to the lack of a fundamental theoretical method. Here, by establishing temperature-dependent transformation thermotics for treating materials whose conductivity depends on temperature, we show analytical and simulation evidence for switchable thermal cloaking and a macroscopic thermal diode based on the cloaking. The latter allows heat flow in one direction but prohibits the flow in the opposite direction, which is also confirmed by our experiments. Our results suggest that the temperature-dependent transformation thermotics could be a fundamental theoretical method for achieving macroscopic heat rectification, and provide guidance both for macroscopic control of heat flow and for the design of the counterparts of switchable thermal cloaks or macroscopic thermal diodes in other fields like seismology, acoustics, electromagnetics, or matter waves., Comment: To be published in Phys. Rev. Lett. (2015); 15 pages, 4 figures