Novel Macroscopic and Microscopic Concepts in Thermoelectricity

Thermoelectric phenomena have been observed for the past two centuries while still being an interesting source of new research because of the countless unknowns governing thermoelectric transport in a host of materials. Novel materials and material structures continue to be discovered, providing enhanced thermoelectric effects that can be used in thermoelectric devices for power generation and refrigeration. With the increasing demand for reusable and renewable energy sources, the importance and usefulness of thermoelectric phenomena grows. It is therefore important to understand thermoelectric transport on both the larger macroscale of devices that serve to define material properties and the smaller microscale where phenomena manifest to give rise to these macroscale properties. In this work, the detailed concepts of macroscopic transformation optics are applied to thermoelectric transport. Using these results, a control of thermoelectric flows is shown that can guide the coupled electric and thermal currents in a predesigned way. Metamaterial designs are given for structures that can cloak, rotate, concentrate, and diffuse the coupled transport. These effects are shown through COMSOL MULTIPHYSICS finite element simulations. The results here show the success of applying transformation optics to control thermoelectric transport. Additionally, the microscopic semiclassical description of thermoelectric transport is explored using multiband wave packets. These multiband wave packets are required to describe transport in material systems with band dispersion degeneracies and are an important generalization of their single band counterparts used in Boltzmann theory. The equations of motion for the real space and reciprocal space positions of these wave packets are derived in the general scenario and are considered in the specific cases of single band transport, degenerate band transport, and a pair of linearly crossing bands. A full model for multiband transport is then developed through the use of a density operator that generalizes the usual Boltzmann transport equation. Expressions for the electric and thermal currents for the case of degenerate bands are then obtained alongside the thermoelectric material properties. This model is currently incomplete but continues to be developed