Thermally Bianisotropic Metamaterials Induced by Spatial Asymmetry

Breaking spatial symmetries can induce interactions between disparate physical fields, which manifest in the macroscopic properties of materials as cross-coupling terms. Prominent examples include Willis terms in phononics and bianisotropic terms in photonics. However, the development of analogous cross-couplings in heat conduction remains limited and incomplete; here, we close this knowledge gap. To this end, we introduce an exact and universal homogenization method to capture the macroscopic dynamics of various physical processes in heterogeneous media. For heat conduction and thermodynamics, the method shows that thermal bianisotropy emerges through the intentional design of spatial asymmetry. In certain conditions, the resulting macroscopic description is free from the infinite heat speed paradox inherent in Fourier's law of conduction. We support the exact theory with examples based on heuristic homogenization of a canonical scattering problem. These results may benefit the design of thermal metamaterials with asymmetric response.