Tunable analog thermal material

Chiral photon blockade in the spinning Kerr resonator

We propose how to achieve chiral photon blockade by spinning a nonlinear optical resonator. We show that by driving such a device at a fixed direction, completely different quantum effects can emerge for the counter-propagating optical modes, due to the spinning-induced breaking of time-reversal symmetry, which otherwise is unattainable for the same device in the static regime. Also, we find that in comparison with the static case, robust non-classical correlations against random backscattering losses can be achieved for such a quantum chiral system. Our work, extending previous works on the spontaneous breaking of optical chiral symmetry from the classical to purely quantum regimes, can stimulate more efforts towards making and utilizing various chiral quantum effects, including applications for chiral quantum networks or noise-tolerant quantum sensors.

Observation of parity-time symmetry in diffusive systems

Phase modulation has scarcely been mentioned in diffusive physical systems because the diffusion process does not carry the momentum like waves. Recently, non-Hermitian physics provides a unique perspective for understanding diffusion and shows prospects in thermal phase regulation, exemplified by the discovery of anti-parity-time (APT) symmetry in diffusive systems. However, precise control of thermal phase remains elusive hitherto and can hardly be realized, due to the phase oscillations. Here we construct the PT-symmetric diffusive systems to achieve the complete suppression of thermal phase oscillation. The real coupling of diffusive fields is readily established through a strong convective background, and the decay-rate detuning is enabled by thermal metamaterial design. We observe the phase transition of PT symmetry breaking with the symmetry-determined amplitude and phase regulation of coupled temperature fields. Our work shows the existence of PT symmetry in dissipative energy exchanges and provides unique approaches for harnessing the mass transfer of particles, wave dynamics in strongly scattering systems, and thermal conduction.

Twisted moiré conductive thermal metasurface

Extensive investigations on the moiré magic angle in twisted bilayer graphene have unlocked the emerging field-twistronics. Recently, its optics analogue, namely opto-twistronics, further expands the potential universal applicability of twistronics. However, since heat diffusion neither possesses the dispersion like photons nor carries the band structure as electrons, the real magic angle in electrons or photons is ill-defined for heat diffusion, making it elusive to understand or design any thermal analogue of magic angle. Here, we introduce and experimentally validate the twisted thermotics in a twisted diffusion system by judiciously tailoring thermal coupling, in which twisting an analog thermal magic angle would result in the function switching from cloaking to concentration. Our work provides insights for the tunable heat diffusion control, and opens up an unexpected branch for twistronics -- twisted thermotics, paving the way towards field manipulation in twisted configurations including but not limited to fluids.

Deep Learning-Assisted Active Metamaterials with Heat-Enhanced Thermal Transport

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, heat-enhanced thermal diffusion metamaterials powered by deep learning is introduced. 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, two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response are designed. 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.

Nonreciprocal Heat Circulation Metadevices

Thermal nonreciprocity typically stems from nonlinearity or spatiotemporal variation of parameters. However, constrained by the inherent temperature-dependent properties and the law of mass conservation, previous works have been compelled to treat dynamic and steady-state cases separately. Here, by establishing a unified thermal scattering theory, the creation of a convection-based thermal metadevice which supports both dynamic and steady-state nonreciprocal heat circulation is reported. The nontrivial dependence between the nonreciprocal resonance peaks and the dynamic parameters is observed and the unique nonreciprocal mechanism of multiple scattering is revealed at steady state. This mechanism enables thermal nonreciprocity in the initially quasi-symmetric scattering matrix of the three-port metadevice and has been experimentally validated with a significant isolation ratio of heat fluxes. The findings establish a framework for thermal nonreciprocity that can be smoothly modulated for dynamic and steady-state heat signals, it may also offer insight into other heat-transfer-related problems or even other fields such as acoustics and mechanics.

Giant, magnet-free, and room-temperature Hall-like heat transfer

Thermal chirality, generically referring to the handedness of heat flux, provides a significant possibility for modern heat control. It may be realized with the thermal Hall effect yet at the high cost of strong magnetic fields and extremely low temperatures. Here, we reveal magnet-free and room-temperature Hall-like heat transfer in an active thermal lattice composed of a stationary solid matrix and rotating solid particles. Rotation breaks the Onsager reciprocity relation and generates giant thermal chirality about two orders of magnitude larger than ever reported at the optimal rotation velocity. We further achieve anisotropic thermal chirality by breaking the rotation invariance of the active lattice, bringing effective thermal conductivity to a region unreachable by the thermal Hall effect. These results could enlighten topological and non-Hermitian heat transfer and efficient heat utilization in ways distinct from phonons.

Non-Hermitian Chiral Heat Transport

Exceptional point (EP) has been captivated as a concept of interpreting eigenvalue degeneracy and eigenstate exchange in non-Hermitian physics. The chirality in the vicinity of EP is intrinsically preserved and usually immune to external bias or perturbation, resulting in the robustness of asymmetric backscattering and directional emission in classical wave fields. Despite recent progress in non-Hermitian thermal diffusion, all state-of-the-art approaches fail to exhibit chiral states or directional robustness in heat transport. Here we report the first discovery of chiral heat transport, which is manifested only in the vicinity of EP but suppressed at the EP of a thermal system. The chiral heat transport demonstrates significant robustness against drastically varying advections and thermal perturbations imposed. Our results reveal the chirality in heat transport process and provide a novel strategy for manipulating mass, charge, and diffusive light.

Observation of bulk quadrupole in topological heat transport

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states-in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics.

Convective Thermal Metamaterials: Exploring High-Efficiency, Directional, and Wave-Like Heat Transfer

Convective thermal metamaterials are artificial structures where convection dominates in the thermal process. Due to the field coupling between velocity and temperature, convection provides a new knob for controlling heat transfer beyond pure conduction, thus allowing active and robust thermal modulations. With the introduced convective effects, the original parabolic Fourier heat equation for pure conduction can be transformed to hyperbolic. Therefore, the hybrid diffusive system can be interpreted in a wave-like fashion, reviving many wave phenomena in dissipative diffusion. Here, recent advancements in convective thermal metamaterials are reviewed and the state-of-the-art discoveries are classified into the following four aspects, enhancing heat transfer, porous-media-based thermal effects, nonreciprocal heat transfer, and non-Hermitian phenomena. Finally, a prospect is cast on convective thermal metamaterials from two aspects. One is to utilize the convective parameter space to explore topological thermal effects. The other is to further broaden the convective parameter space with spatiotemporal modulation and multi-physical effects.

Homogeneous Zero-Index Thermal Metadevice for Thermal Camouflaging and Super-Expanding

The infinite effective thermal conductivity (IETC) can be considered to be an equivalence of the effective zero index in photonics. A recent highly rotating metadevice has been discovered to approach near IETC, subsequently demonstrating a cloaking effect. However, this near IETC, related to a rotating radius, is quite inhomogeneous, and the high-speed rotating motor also needs a high energy input, limiting its further applications. Herein, we propose and realize an evolution of this homogeneous zero-index thermal metadevice for robust camouflaging and super-expanding through out-of-plane modulations rather than high-speed rotation. Both the theoretical simulations and experiments verify a homogeneous IETC and the corresponding thermal functionalities beyond cloaking. The recipe for our homogeneous zero-index thermal metadevice involves an external thermostat, which can be easily adjusted for various thermal applications. Our study may provide meaningful insights into the design of powerful thermal metadevices with IETCs in a more flexible way.

Black-hole-inspired thermal trapping with graded heat-conduction metadevices

The curved space-time produced by black holes leads to the intriguing trapping effect. So far, metadevices have enabled analogous black holes to trap light or sound in laboratory spacetime. However, trapping heat in a conductive environment 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 an insight into correlating transformation thermotics with other disciplines, such as cosmology, for emerging heat control schemes.

Tunable liquid-solid hybrid thermal metamaterials with a topology transition

Thermal metamaterials provide rich control of heat transport which is becoming the foundation of cutting-edge applications ranging from chip cooling to biomedical. However, due to the fundamental laws of physics, the manipulation of heat is much more 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 findings illustrate the extraordinary heat transport in complex multicomponent thermal metamaterials and pave the way toward an unprecedented regime of heat manipulation.

Biphysical undetectable concentrators manipulating both heat flux and direct current via topology optimization

Recent remarkable developments in metamaterials and metadevices manipulating diffusive processes, such as thermal and electrical conduction, have enabled the control of multiple phenomena and the development of multifunctional devices. However, only either multiphysics operations or multiple functionalities are usually implemented on single metadevices. In this paper, we describe a method for the optimal design of metadevices that achieves both cloaking and focusing in the control of both heat flux and direct current by a single device, i.e., biphysical-bifunctional metadevices having four capabilities. Our design scheme performs well in terms of providing cloaking and focusing bifunctionality. Additionally, it assumes bulk natural materials without the use of metamaterials, which improves the manufacturability of the designed metadevices. Moreover, multidirectional metad evices are optimally designed for thermal-electrical conductions transmitted from multiple directions or from heat and voltage sources at various locations.

Thermal Willis Coupling in Spatiotemporal Diffusive Metamaterials

Willis coupling generically stems from bianisotropy or chirality in wave systems. Nevertheless, those schemes are naturally unavailable in diffusion systems described by a single constitutive relation governed by the Fourier law. Here, we report spatiotemporal diffusive metamaterials by modulating thermal conductivity and mass density in heat transfer. The Fourier law should be modified after homogenizing spatiotemporal parameters, featuring thermal Willis coupling between heat flux and temperature change rate. Thermal Willis coupling drives asymmetric heat diffusion, and the diffusion direction is reversible at a critical point determined by the degree of spatiotemporal modulation. Moreover, thermal Willis coupling stands robustly even when only thermal conductivity is modulated. These results may have potential applications for directional diffusion and offer insights into asymmetric manipulation of nonequilibrium mass and energy transfer.

Geometric Phase and Localized Heat Diffusion

Many unusual wave phenomena in artificial structures are governed by their topological properties. However, the topology of diffusion remains almost unexplored. One reason is that diffusion is fundamentally different from wave propagation because of its purely dissipative nature. The other is that the diffusion field is mostly composed of modes that extend over wide ranges, making it difficult to be rendered within the tight-binding theory as commonly employed in wave physics. Here, the above challenges are overcome and systematic studies are performed on the topology of heat diffusion. Based on a continuum model, the band structure and geometric phase are analytically obtained without using the tight-binding approximation. A deterministic parameter is found to link the geometric phase with the edge state, thereby proving the bulk-boundary correspondence for heat diffusion. The topological edge state is experimentally demonstrated as localized heat diffusion and its dependence on the boundary conditions is verified. This approach is general, rigorous, and able to reveal rich knowledge about the system with great accuracy. The findings set up a solid foundation to explore the topology in novel thermal management applications.

A Real-Time Self-Adaptive Thermal Metasurface

Emerging metamaterials have served as an efficient strategy for the realization of unconventional heat control and management using structural thermal properties, and many functional thermal metadevices have been investigated. However, thermal functions are usually fixed or limited in the switching range. Thus far, real-time thermal regulation is elusive for thermal metamaterials because of deterministic artificial metastructures and uncontrollable phase transitions, coupled with the absence of dynamic adaptability. Here, a self-adaptive metasurface platform to implement programmable thermal functions via the automatic evolution of thermoelectric heat sources and real-time control of the driven voltage is reported. The proof-of-concept smart platform experimentally demonstrates arbitrary switching between elaborate thermal patterns consolidated into an active thermoelectric element matrix. Further, thermal pixels and feedback control systems are integrated into printed circuit boards, resulting in self-adaptability to any thermal requirements. This study sets up a new paradigm for arbitrary transitions between exquisite thermal patterns and is expected to pave the way for real-time thermal management in a programming formation.

Heat transfer control using a thermal analogue of coherent perfect absorption

Recent investigations on non-Hermitian physics have unlocked new possibilities to manipulate wave scattering on lossy materials. Coherent perfect absorption is such an effect that enables all-light control by incorporating a suitable amount of loss. On the other hand, controlling heat transfer with heat may empower a distinct paradigm other than using thermal metamaterials. However, since heat neither propagates nor carries any momentum, almost all concepts in wave scattering are ill-defined for steady-state heat diffusion, making it formidable to understand or utilize any coherent effect. Here, we establish a scattering theory for heat diffusion by introducing an imitated momentum for thermal fields. The thermal analogue of coherent perfect absorption is thus predicted and demonstrated as the perfect absorption of exergy fluxes and undisturbed temperature fields. Unlike its photonic counterpart, thermal coherent perfect absorption can be realized for regular thermal materials, and be generalized for various objects.

A thermal analogue of coherent perfect absorption would allow to control heat transfer using heat, but the lack of momentum propagation in a thermal field seems to prevent any role for coherence. Here, the authors allow this by introducing an imitated momentum for steady-state heat diffusion.

Design of an omnidirectional camouflage device with anisotropic confocal elliptic geometry in thermal-electric field

The designed confocal elliptical core-shell structure can realize the omnidirectional camouflage effect without disturbing temperature and electric potential profiles as the directions of heat flux and electric current change. Based on the anisotropy of the confocal ellipse, the anisotropic effective parameters of the confocal elliptical core-shell structure are derived under different heat flux and electric current launching. Then, the matrix material should be anisotropic as the effective parameters to satisfy the omnidirectional camouflage effect, which is demonstrated numerically. In addition, we present a composite structure to realize the anisotropic matrix. The experimental results show that the camouflage device embedded in the composite structure can eliminate the scattering caused by the elliptical core under different directions of heat flux and electric current, thus achieving the omnidirectional thermal-electric camouflage effect experimentally. The omnidirectional camouflage effect in thermal and electric fields can greatly widen the application fields of this device with anisotropic geometry.

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Omnidirectional camouflage device with anisotropic geometry is constructed

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Anisotropic matrix dominates the thermal-electric camouflage effect omnidirectionally

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A multilayered composite structure contributes to the experimental implementation

Observation of Weyl exceptional rings in thermal diffusion

Thermal diffusion is dissipative and strongly related to non-Hermitian physics. At the same time, non-Hermitian Weyl systems have spurred tremendous interest across photonics and acoustics. This correlation has been long ignored and hence shed little light upon the question of whether the Weyl exceptional ring (WER) in thermal diffusion could exist. Intuitively, thermal diffusion provides no real parameter dimensions, thus prohibiting a topological nature and WER. This work breaks this perception by imitating synthetic dimensions via two spatiotemporal advection pairs. The WER is achieved in thermal diffusive systems. Both surface-like and bulk states are demonstrated by coupling two WERs with opposite topological charges. These findings extend topological notions to diffusions and motivate investigation of non-Hermitian diffusive and dissipative control.

A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.

Diffusive Fizeau Drag in Spatiotemporal Thermal Metamaterials

Fizeau drag means that the speed of light can be regulated by the flow of water, owing to the momentum interaction between photons and moving media. However, the dragging of heat is intrinsically elusive, due to the absence of momentum in thermal diffusion. Here, we design a spatiotemporal thermal metamaterial based on heat transfer in porous media to demonstrate the diffusive analog to Fizeau drag. The space-related inhomogeneity and time-related advection enable the diffusive Fizeau drag effect. Thanks to the spatiotemporal coupling, different propagating speeds of temperature fields can be observed in two opposite directions, thus facilitating nonreciprocal thermal profiles. The phenomenon of diffusive Fizeau drag stands robustly even when the direction of advection is perpendicular to the propagation of temperature fields. These results could pave an unexpected way toward realizing the nonreciprocal and directional transport of mass and energy.

Passive Ultra-Conductive Thermal Metamaterials

Ultra-conductive heat transport showcases significant potentials in popular thermal managements with convection, phase change, and heat source. However, it is captivated impossible for passive thermal manipulation, usually bounded by intrinsic thermal conductivities of natural materials, to outperform these active recipes in need of extra energy payload. Here, a robust recipe to create passive ultra-conductive thermal metamaterials consisting of nothing but bulk natural materials is reported. Thanks to the local thermal resistance regulation by vertical thermal transport channel, the proof-of-concept thermal metamaterials experimentally demonstrate extreme effective conductivity (1915 W m^-1  K^-1 ) solely with naturally occurring materials. The purely conductive modulation without any external energy is comparable to active counterparts, and further reveals its robustness and unexpected convenience. The findings construct a high-efficient paradigm of passive thermal management with ultra-conductive heat transport, and further hint potentials in other Laplace fields, e.g., DC and magnetostatics.

Thermal Cloak: Theory, Experiment and Application

In the past two decades, owing to the development of metamaterials and the theoretical tools of transformation optics and the scattering cancellation method, a plethora of unprecedented functional devices, especially invisibility cloaks, have been experimentally demonstrated in various fields, e.g., electromagnetics, acoustics, and thermodynamics. Since the first thermal cloak was theoretically reported in 2008 and experimentally demonstrated in 2012, great progress has been made in both theory and experiment. In this review, we report the recent advances in thermal cloaks, including the theoretical designs, experimental realizations, and potential applications. The three areas are classified according to the different mechanisms of heat transfer, namely, thermal conduction, thermal convection, and thermal radiation. We also provide an outlook toward the challenges and future directions in this fascinating area.

Robustly printable freeform thermal metamaterials

Thermal metamaterials have exhibited great potential on manipulating, controlling and processing the flow of heat, and enabled many promising thermal metadevices, including thermal concentrator, rotator, cloak, etc. However, three long-standing challenges remain formidable, i.e., transformation optics-induced anisotropic material parameters, the limited shape adaptability of experimental thermal metadevices, and a priori knowledge of background temperatures and thermal functionalities. Here, we present robustly printable freeform thermal metamaterials to address these long-standing difficulties. This recipe, taking the local thermal conductivity tensors as the input, resorts to topology optimization for the freeform designs of topological functional cells (TFCs), and then directly assembles and prints them. Three freeform thermal metadevices (concentrator, rotator, and cloak) are specifically designed and 3D-printed, and their omnidirectional concentrating, rotating, and cloaking functionalities are demonstrated both numerically and experimentally. Our study paves a powerful and flexible design paradigm toward advanced thermal metamaterials with complex shapes, omnidirectional functionality, background temperature independence, and fast-prototyping capability.

Configurable Phase Transitions in a Topological Thermal Material

Diffusive nature of thermal transportation fundamentally restricts topological characteristics due to the absence of a sufficient parametric space with complex dimensionalities. Here, we create an orthogonal advection space with two advective pairs to reveal the unexplored topological transitions in thermal material. We demonstrate four types of configurable thermal phases, including the nontrivial dynamic-equilibrium distribution, nonchiral steplike π-phase transition, and another two trivial profiles related to the anti-parity-time symmetry nature. Our findings provide a recipe for realizing a topologically robust thermal system under arbitrary perturbations.