Correlated thermoelectrics

Abstract. In the first part of these lecture notes we introduce the phenomenological equations for describing the heat and charge transport in thermoelectric samples. We discuss the solution obtained for various boundary conditions that are appropriate for the homogeneous and inhomogeneous thermoelectrics. In the second part we develop the formalism for a linear-response many-body description of the transport properties of correlated electrons. By properly determining the local heat-current operator we show that the Jonson-Mahan theorem applies to the Hamiltonians that are commonly used for the intermetallic compounds with Cerium, Europium and Ytterbium ions, so the various thermal-transport coefficient integrands are related by powers of frequency. We illustrate how to use this formalism by calculating the thermoelectric properties of the periodic Anderson model and, then, show that these results explain the experimental data on heavy fermions and valence fluctuators. Finally, we calculate the thermoelectric properties of the Falicov-Kimball model and use the results to explain the anomalous features of the intermetallic compounds in which one observes the valence-change transition