Configurable Phase Transitions in a Topological Thermal Material

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.

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.

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.

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.

Controlling Local Thermal States in Classical Many-Body Systems

The process of thermalization in many-body systems is driven by complex interactions among subsystems and a surrounding environment. Here we lay the theoretical foundations for the active control of local thermal states in arbitrary nonreciprocal systems close to their equilibrium state. In particular we describe how to (i) force some part of the system to evolve according to a prescribed law during the relaxation process (i.e., thermal targeting probem), (ii) insulate some elements from the rest of the system, or (iii) synchronize their evolution during the relaxation process. We also derive the general conditions a system must fulfill in order that some parts relax toward a minimal temperature with a minimum energetic cost or relax toward a prescribed temperature with a minimum time. Finally, we consider several representative examples in the context of systems exchanging heat radiatively.

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.

Geometric heat pump and no-go restrictions of nonreciprocity in modulated thermal diffusion

Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.

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.

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.

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.