Manipulating multiphysical fields with metamaterials has received enormous attention recently because of the high functional integration and extensive practical applicability. However, coupled multi-field systems such as thermoelectric fields, where heat and electric fluxes are coupled via the Seebeck coefficients, still lack efficient control with artificial structures. Here, we theoretically design a category of bilayer thermoelectric metamaterials based on the generalized scattering-cancellation method. By solving the governing equations directly, we formulate the specific parameter requirements for the desired functionalities beyond existing single-field or decoupled multi-field Laplacian metamaterials. Compared with the recently reported transformation optics for thermoelectric flows, bilayer schemes do not require inhomogeneity and anisotropy in constitutive materials. Finite-element simulations confirm the analytical results and show robustness under various exterior conditions. A feasible experimental design with naturally occuring materials is also proposed for further proof-of-principle verification. Our theoretical method and device design may be extended to other coupled multiphysical systems such as thermo-optics, thermomagnetics, optomechanics, etc.
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