Transformation Optics for Thermoelectric Transport

Transformation optics has proven to be an effective technique in manipulating electromagnetic fields, heat and electrical currents, and other physical phenomena by utilizing coordinate transformation methods. This has been a powerful approach in the design of cloaks, field rotators, and concentrators, which have also been implemented in novel devices. We show that transformation optics can also be applied to coupled thermal and electric transport as captured in thermoelectricity. The description relies on the invariance of the thermodynamic governing and constitutive equations for thermoelectricity. We demonstrate that the thermoelectric flow can be cloaked, rotated, or concentrated by specifying appropriate coordinate transformations. The design of metamaterial composites constructed using bilayer components with specified transport properties realizing such thermoelectric flow is also considered. The proposed thermoelectric cloak, rotator, and concentrator are independent of the particular boundary conditions and can also operate in (decoupled) electric or heat modes.