Based on a first-principles approach, we exploit a class of shaped graded materials in which thermal energy is apparently controlled to transfer from a region of lower temperature to a region of higher temperature. This phenomenon, which is in contrast to our common intuition, is indicative of an apparent negative thermal conductivity (ANTC). Further analysis shows that the ANTC is related to a symmetric oscillation of paired thermal conductivities with specific gradation profiles, which are shown to satisfy a sum rule. Such shaped graded materials can serve as good candidates for thermal rectification.

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 it could provide guidance both for the 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, and matter waves.

We theoretically explore a type of bifunctional cloak possessing both electrical and thermal cloaking functionality. We employ a composite material to design the cloak shell. By using effective medium theory, the effective electrical and thermal conductivities of the composite material should meet the perfect conductivity profile calculated from the coordinate transformation approach. In the design, we choose nonspherical nanoparticles with appropriate electrical and thermal conductivities, shape aspects, and volume fractions. Furthermore, finite element simulations are performed to verify the properties of such bifunctional cloaks.

Diffusion driven by temperature or concentration gradients is a fundamental mechanism of energy and mass transport that 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 that expanded the original concepts and suggested innovative metamaterial-based devices. The term diffusionics is used in the review to generalize these noteworthy achievements in various energy and mass diffusion systems. Examples include heat diffusion systems and particle and plasma diffusion systems. For clarity the numerous studies published over the past decade are categorized by diffusion field (i.e., heat, particles, and plasmas) and discussed 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 interesting metamaterial-based devices, such as cloaks and radiative coolers; and the physics perspective, to connect them with concepts of recent concern, such as non-Hermitian topology, nonreciprocal transport, and spatiotemporal modulation. The possibility of controlling diffusion processes beyond metamaterials is also discussed. Finally, several future directions for diffusion metamaterial research, including the integration of metamaterials with artificial intelligence and topology concepts, are examined.

Thermal metamaterials have amazing properties in heat transfer beyond naturally occurring materials owing to their well-designed artificial structures. The idea of thermal metamaterial has completely subverted the design of thermal functional devices and makes it possible to manipulate heat flow at will. In this perspective, we review the up-to-date progress of thermal metamaterials starting from 2008. We focus on both the key theoretical fundamentals and techniques for applications and give a perspective of scale-based classification on thermal metamaterials' theories and applications. We also discuss the junction between macroscale and microscale design methods and propose some prospects for the future trend of this field.