Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields

The full control of single or even multiple physical fields has attracted intensive research attention in the past decade, thanks to the development of metamaterials and transformation optics. Significant progress has been made in vector fields (e.g., optics, electromagnetics, and acoustics), leading to a host of strikingly functional metamaterials, such as invisibility cloaks, illusion devices, concentrators, and rotators. However, metamaterials in vector fields, designed through coordinate transformation of Maxwell's equations, usually require extreme parameters and impose challenges on the actual realization. In this context, metamaterials in scalar fields (e.g., thermal and dc fields), which are mostly governed by the Laplace equation, lead to more plausible and facile implementations, since there are native insulators and excellent conductors (serving as two extreme cases). This paper therefore is particularly dedicated to reviewing the most recent advances in Laplacian metamaterials in manipulating thermal (both transient and steady states) and dc fields, separately and (or) simultaneously. We focus on the theory, design, and realization of thermal/dc functional metamaterials that can be used to control heat flux and electric current at will. We also provide an outlook toward the challenges and future directions in this fascinating area.