Programmable Electrothermal Quad-Functional Metamaterials for Decoupled Multi-Field Control

The extension of multifunctional metamaterials to coupled electro-thermal systems holds the potential for transformative applications in adaptive camouflage, energy transport, and microelectronics. However, strong electron-phonon interactions and the intrinsic coupling between voltage-current and temperature-heat flux fields limit existing designs to one or two functionalities. Here, we report a field-line-guided coordinate transformation strategy for constructing an electrothermal quad-functional metamaterial (ETQFM) capable of simultaneously controlling current, voltage, heat flux, and temperature fields within a single architecture. By mapping prescribed field trajectories into spatially distributed material-geometry configurations, the transformation decouples electrical and thermal responses, enabling independent realization of cloaking, concentrator, and rotation across both domains. As a proof of concept, six distinct prototypes are fabricated by 3D printing of laser-sintered metal powders and experimentally validate, each exhibiting four independent functions with high fidelity and agreement with simulations. The strategy also allows functional switching in symmetric architectures by rotating boundary conditions and remains robust against low-power thermal perturbations, establishing a generalizable framework for multi-physics field manipulation.