Dynamic reconfigurable metamaterials for coordinated heat and charge transport

Coordinated control of coupled heat and charge transport is fundamental to advanced thermoelectric energy conversion and management. Existing thermoelectric metamaterials are largely limited to static or steady-state functionalities. While spatiotemporal modulation has enabled dynamic regulation of single diffusion fields, extending such control to coupled thermoelectric systems remains challenging due to the intrinsic coupling via the Seebeck and Peltier effects and the vastly different thermal and electrical timescales. A unified theoretical framework for designing physically consistent, dynamically reconfigurable thermoelectric devices under transient conditions is lacking. Here, we establish a time-dependent transformation theory for coupled thermoelectric fields. We prove that the governing equations retain form invariance under coordinate transformations even when material parameters vary in space and time, and derive transformation rules for thermal conductivity, electrical conductivity, heat capacity, and the Seebeck coefficient. This enables the systematic design of dynamic thermoelectric functionalities through spacetime-dependent coordinate mappings. We numerically demonstrate three representative functionalities—cloaking, concentration, and rotation—in which heat flux and electric current are manipulated simultaneously without disturbing external fields. Furthermore, we design a time-adjustable thermoelectric cloak-concentrator by introducing a time-dependent virtual radius. For experimental realization, we propose a rotatable checkerboard structure based on effective-medium theory that exhibits periodic switching between cloaking and concentrating modes using conventional metals. This work provides a unified framework for designing dynamically reconfigurable thermoelectric devices, transcending the functionality-fixed limitation of conventional metamaterials. The theory is generalizable to other coupled diffusion processes, opening avenues for adaptive energy routing, intelligent thermal management, and spatiotemporal information processing.