In recent years, there have been important developments in the design and fabrication of new thermoelectrics. While a decade ago, progress was mainly empirical, recent advances in theoretical methods have led to a deeper understanding of the parameters that affect the performance of materials in thermoelectric devices. These have brought the goal of producing materials with the required characteristics for commercial application a significant step closer. A search
for efficient materials requires a fully microscopic treatment of the charge and heat transport, and the aim of this book is to explain all thermoelectric phenomena from this modern quantum-mechanical perspective.
In the first part on phenomenology, conjugate current densities and forces are derived from the condition that the rate of change of the entropy density of the system in the steady state is given by the scalar product between them. The corresponding transport coefficients are explicitly shown to satisfy Onsager's reciprocal relations. The transport equations are solved for a number of cases, and the coefficient of performance, the efficiency, and the figure of merit are computed.
State-of-the-art methods for the solution of the transport equations in inhomogeneous thermoelectrics are presented. A brief account on how to include magnetization transport in the formalism is also given.
In the second part, quantum mechanical expressions for the transport coefficients are derived, following the approach by Luttinger. These are shown to satisfy Onsager's relations by construction. Three lattice models, currently used to describe strongly correlated electron systems, are introduced: the Hubbard, the Falicov-Kimball, and the periodic Anderson model (PAM), and the relevant current density operators are derived for each of them. A proof of the Jonson-Mahan theorem, according to
which all transport coefficients for these models can be obtained from the integral of a unique transport function multiplied by different powers of the frequency, is given.
The third part compares theory and experiment. First for the thermoelectric properties of dilute magnetic alloys, where the theoretical results are obtained from poor man's scaling solutions to single impurity models. Then it is shown that the experimental data on heavy fermions and valence fluctuators are well reproduced by the transport coefficients computed for the PAM at low and high temperature. Finally, results obtained from first principles calculations are shown, after a short
introduction to density functional theory and beyond. A number of useful appendices complete the book.
Born in 1945, Veljko Zlatic studied physics in Zagreb and obtained his first degree from Zagreb University in 1969. From 1970 to 1974 he studied theoretical physics at Imperial College and obtained his PhD. He taught many body physics at Zagreb University from 1974 to 1999. He was Humboldt Fellow at Frankfurt University in 1980/81 and Berlin University in 1989, Visiting Fellow at Oxford University in 1993/1994, and Visiting Professor at Georgetown University 1996/97 and 2006/07. He retired as a Senior Scientist from the Institute of Physics in 2010. His main research interest is the theoretical description of strongly correlated materials. Born in 1946, Rene Monnier obtained his Diploma in Physics with honours from the University of Neuchatel in 1970. He was a Visiting Fellow at Cornell University from January 1971 to July 1972, after which he returned to Neuchatel, where he defended his thesis in April 1974. From October 1975 to July 1977 he was a postdoctoral fellow at Nordita, in Copenhagen. He joined ETH in October 1977 and was awarded the Professor title in 2000. His field of research is condensed matter theory, and his main interests lie in the study of the electronic structure and properties of random alloys and their surfaces, exotic compounds and strongly correlated systems. He has taught graduate courses on these subjects as well as introductory physics to students in engineering and in the life sciences.
PART I: CLASSICAL THEORY; PART II: QUANTUM THEORY; PART III: COMPARISON OF THEORY AND EXPERIMENT