Diffusive Fizeau Drag in Spatiotemporal Thermal Metamaterials

Broadband nonreciprocal thermal emissivity and absorptivity

A body that violates Kirchhoff's law of thermal radiation exhibits an inequality in its spectral directional absorptivity and emissivity. Achieving such an inequality is of fundamental interest as well as a prerequisite for achieving thermodynamic limits in photonic energy conversion1 and radiative cooling2. Thus far, inequalities in the spectral directional emissivity and absorptivity have been limited to narrow spectral resonances3, or wavelengths well beyond the infrared regime4. Bridging the gap from basic demonstrations to practical applications requires control over a broad spectral range of the unequal spectral directional absorptivity and emissivity. In this work, we demonstrate broadband nonreciprocal thermal emissivity and absorptivity by measuring the thermal emissivity and absorptivity of gradient epsilon-near-zero InAs layers of subwavelength thicknesses (50 nm and 150 nm) with an external magnetic field. The effect occurs in a spectral range (12.5-16 μm) that overlaps with the infrared transparency window and is observed at moderate (1 T) magnetic fields.

Nonreciprocal Topological Phonon Transfer Independent of Both Device Mass and Exceptional-Point Encircling Direction

Imposing topological operations encircling an exceptional point (EP) engenders unconventional one-way topological phonon transfer (TPT), strictly depending on the direction of EP-inclusive control loops and inherently limited to the small-mass regime of practical resonators. We here show how to beat these limitations and predict a mass-free unidirectional TPT by combining topological operations with the Fizeau light-dragging effect, which splits countercirculating optical modes. An efficient TPT happens when light enters from one chosen side of the fiber but not from the other, leading to a unique nonreciprocal TPT, independent of the direction of winding around the EP. Unlike previous proposals naturally sensitive to both mass and quality of quantum devices, our approach is almost immune to these factors. Remarkably, its threshold duration of adiabatic control loops for maintaining an optimal TPT can be easily shortened, yielding a top-speed-tunable perfect TPT that has no counterpart in previous demonstrations. The study paves a quite-general route to exploiting profoundly different chiral topological effects, independent of both EP-encircling direction and device mass.

Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems

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 Schrödinger equation and diffusion equation, research on higher-order topological insulators has 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." Because of the anti-Hermitian properties of diffusive Hamiltonian, we investigate the thermal behavior of these corner states through theoretical calculation, simulation, and experiment. Furthermore, we study the different thermal behaviors 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.

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.

Thermal conduction force under standing and quasistanding temperature field

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 wavelike 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 quasistanding temperature fields, revealing distinct characteristics of thermal conduction force. Moreover, we establish a link between the progressive and standing cases through the quasistanding 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.

Achieving Environmentally-Adaptive and Multifunctional Hydrodynamic Metamaterials through Active Control

As hydrodynamic metamaterials continue to develop, the inherent limitations of passive-mode metamaterials become increasingly apparent. First, passive devices are typically designed for specific environments and lack the adaptability to environmental changes. Second, their unique functions often rely on intricate structures, or challenging material properties, or a combination of both. These limitations considerably hinder the potential applications of hydrodynamic metamaterials. In this study, an active-mode hydrodynamic metamaterial is theoretically proposed and experimentally demonstrated by incorporating source-and-sink flow-dipoles into the system, enabling active manipulation of the flow field with various functionalities. By adjusting the magnitude and direction of the flow-dipole moment, this device can easily achieve invisibility, flow shielding, and flow enhancing. Furthermore, it is environmentally adaptive and can maintain proper functions in different environments. It is anticipated that this design will significantly enhance tunability and adaptability of hydrodynamic metamaterials in complex and ever-changing environments.

Enhancement of near-field thermal radiation between composite materials with gradient plasmonic nanoparticles

Near-field radiative heat transfer (NFRHT) with composite materials is of significant technological interest for practical applications. In this study, we investigate the NFRHT occurring between two composite materials composed of gradient plasmonic nanoparticles (GPNs). We delve into the physical mechanism underlying NFRHT, highlighting the strong coupling and enhancement effect from surface plasmon polaritons (SPPs) at the composite/air interface or the localized SPPs (LSPPs) on the surface of nanoparticles. Furthermore, leveraging the red-shift effect caused by the gradient profile, the intensity of NFRHT can be controlled by adjusting the gradient function and volume fraction of GPNs. Notably, we observe the enhancement of NFRHT from composite materials to bulk materials, with the enhancement ratio exhibiting a notable increase at large spacing. This research establishes a theoretical foundation for the development of near-field thermal devices utilizing composite materials containing GPNs.

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.

Adaptive multi-temperature control for transport and storage containers enabled by phase-change materials

The transportation of essential items, such as food and vaccines, often requires adaptive multi-temperature control to maintain high safety and efficiency. While existing methods utilizing phase change materials have shown promise, challenges related to heat transfer and materials' physicochemical properties remain. In this study, we present an adaptive multi-temperature control system using liquid-solid phase transitions to achieve highly effective thermal management using a pair of heat and cold sources. By leveraging the properties of stearic acid and distilled water, we fabricated a multi-temperature maintenance container and demonstrated temperature variations of only 0.14-2.05% over a two-hour period, underscoring the efficacy of our approach. Our findings offer a practical solution to address critical challenges in reliable transportation of goods, with potential implications for various fields in physical, engineering, and life sciences.

Tunable thermal conduction force without macroscopic temperature gradients

Ubiquitous thermal conduction makes its force effect particularly important in diverse fields, such as electronic engineering and biochemistry. However, regulating thermal conduction force is still challenging due to two stringent restrictions. First, a temperature gradient is essential for inducing the force effect. Second, the force direction is fixed to the temperature gradient in a specific material. Here, we demonstrate that thermal conduction force can exist unexpectedly at a zero average temperature gradient in dielectric crystals. The wavelike feature of thermal conduction is considered, i.e., the second sound mode. Based on the momentum conservation law for phonon gases, we analyze thermal conduction force with the plane, zeroth-order Bessel, and first-order Bessel second sounds. Remarkably, the force direction is highly tunable to be along or against the second sound direction. These results provide valuable insights into thermal conduction force in those environments with temperature fluctuations, and they open up possibilities for practical applications in manipulating the local thermal conductivity of crystals.

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.

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.

Near-Infrared Trapping by Surface Plasmons in Randomized Platinum-Ceramic Metamaterial for Thermal Barrier Coatings

As the operation temperature of next generation gas turbine is targeted to be 1800 °C toward a higher efficiency and lower carbon emission, the near-infrared (NIR) thermal radiation becomes a major concern for the durability of the metallic turbine blades. Although thermal barrier coatings (TBCs) are applied to provide thermal insulations, they are translucent to the NIR radiation. It is a major challenge for TBCs to achieve optically thick with limited physical thickness (usually < 1 mm) for effectively shielding the NIR radiation damage. Here, an NIR metamaterial is reported, where a Gd₂ Zr₂ O₇ ceramic matrix is randomly dispersed with microscale Pt (0.53 vol%) nanoparticles with a size of 100-500 nm. Attenuated by the Gd₂ Zr₂ O₇ matrix, a broadband NIR extinction is achieved through the red-shifted plasmon resonance frequencies and higher-order multipole resonances of the Pt nanoparticles. A very high absorption coefficient of ≈3 × 10⁴ m^-1 , approaching the Rosseland diffusion limit for a typical coating thickness, minimizes the radiative thermal conductivity to ≈10^-2  W m^-1 K^-1 and successfully shields the radiative heat transfer. This work suggests that constructing a conductor/ceramic metamaterial with tunable plasmonics could be a strategy to shield NIR thermal radiation for high temperature applications.

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.

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 Rectification of Diffusion-Wave Fields by Spatiotemporal Metamaterials

The diffusion process is the basis of many branches of science and engineering, and generally obeys reciprocity between two ports of a linear time-invariant medium. Recent research on classical wave dynamics has explored the spatiotemporal modulation to exhibit preferred directions in photons and plasmons. Here we report a distinct rectification effect on diffusion-wave fields by modulating the conductivity and observe nonreciprocal transport of charges. We experimentally create a spatiotemporal diffusion metamaterial, in which a mode transition to zero frequency is realized. A direct current component thereby emerges, showcasing a biased effect on the charge diffusion when the incident fundamental frequency is a multiple of the system modulation frequency. These results may find applications spanning a plethora of diffusive fields in general.

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.

Nonlinear thermal responses in geometrically anisotropic metamaterials

Nonlinear metamaterials have great potential in heat management, which has aroused intensive research interest in both theory and application, especially for their response to surroundings. However, most existing works focus on geometrically isotropic (circular) structures, limiting the potential versatile functionalities. On the other hand, anisotropy in architecture promisingly offers an additional degree of freedom in modulating directional heat transfer. Here, we investigate nonlinear composition effects in geometrically anisotropic (confocal elliptical) thermal medium under the framework of effective medium approximation, and deduce a series of general formulas for quantitatively predicting nonlinearity enhancement. Enhancement coefficients are analytically derived by the Taylor expansion method in different nonlinearity cases. In particular, we find that some coupling conditions can greatly promote the nonlinear modulation coefficients, introducing stronger enhancement beyond isotropic construction. Our theoretical predictions are verified by finite-element simulation, and feasible experimental suggestions are also given. For extending these results to practical scenes, two intelligent thermal metadevices are designed in proof of concept and demonstrated by numerical simulation. Our works provide a unified theory for anisotropic nonlinear thermal metamaterial design and may benefit flexible applications in self-adaptive thermal management, such as switchable cloaks, concentrators, or macroscopic thermal diodes.

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.