Thermoelectricity of Quantum Matter

The discovery of thermoelectricity - the interdependence of an electric field and a temperature gradient in a solid - is almost two centuries old. But our understanding of the basic microscopic physics behind thermoelectric phenomena is still too sketchy to yield an accurate quantitative description of the thermoelectric response and its temperature and field dependence even in simple metals. As a consequence, the quest for useful thermoelectric materials has been mostly an empiric one. A recent surge in this quest, partly motivated by the environment- friendliness of thermoelectric refrigerators and generators, is visible across the worldwide scientific community. From the fundamental point of view, during the last decade, thermoelectricity has proved to be a very sensitive, even if poorly understood, probe of electron organization in solids, in particular in the context of electron correlation. Thermoelectricity of quantum materials is largely unexplored. There are technical reasons for this. Nowadays, commercial instruments permit to measure the electrical resistivity or specific heat of materials in wide temperature ranges, with high resolution. Accurate low-temperature and high-field measurements of the Seebeck and the Nernst effect, and of the thermal conductivity, however, require a level of experimental sophistication well beyond what is commercially available. The two partners are among a handful of leading groups on the international scene exploring the thermoelectric response of correlated electrons under extreme conditions. The aim of this project is to initiate a new collaboration in order to carry out high-resolution thermoelectric measurements in a number of quantum materials. Experimentally ambitious, the scientific scope of the proposal covers a number of issues which are at the heart of the physics of correlated electrons: Quantum criticality in heavy fermion compounds and in graphite, the residual electronic density of states in Kondo insulators and possible relations to metallic surface states of topological insulators, and semimetals pushed beyond the quantum limit. The results are expected to provide fresh experimental input for a deeper theoretical understanding of electronic correlations and thermoelectric phenomena, and ultimately for advancing the field of thermoelectric and thermomagnetic refrigeration.

Thermoelectricity is the property of solids to directly convert temperature differences into electricity. What sounds like a simple recipe to produce a thermoelectric generator is based on an intricate interplay between electrical and thermal fields in the solid that tells us much about its fundamental nature. To use thermoelectric measurements to understand fundamental processes in quantum materials was the key motivation of the project.In a joint effort two research teams, based in Paris and Vienna, together with their network of international collaborators, studied selected quantum materials of particular current interest. The French team focused on weakly correlated semimetals, topological insulators, and superconductors, the Viennese team on strongly correlated metals, semimetals, and semiconductors. Thermoelectric measurements under the conditions needed to study these materials frequently very low temperatures and high magnetic fields are extremely challenging. The intense exchange between both groups was essential to bring such experiments to perfection, both in home-made setups and at high-field facilities. Key results on the strongly correlated systems (Vienna) include a better understanding of how quantum phases transform into one-another, both in metals and in insulators, how residual low-temperature conductivity can emerge in correlated insulators, and how even phonons can acquire strongly correlated properties. These insights trigger new fundamental questions, and may help to design better materials for practical applications in the field of thermoelectricity.