Modern Theory of Thermoelectricity

Hardcover | June 22, 2014

byVeljko Zlatic, Rene Monnier

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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 materialsin 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 isto 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 tosatisfy 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 arepresented. 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 uniquetransport 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 valencefluctuators 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 thebook.

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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 materialsin thermoelectric devices. These have brough...

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...
Format:HardcoverDimensions:304 pages, 9.69 × 6.73 × 0.01 inPublished:June 22, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198705417

ISBN - 13:9780198705413

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Table of Contents

IntroductionPart I: Classical theory1. Phenomenological description of thermoelectric phenomena2. Phenomenological transport equations3. Physical interpretation4. Thermomagnetic and galvanomagnetic effects5. Solutions of the transport equations for homogenous thermoelectrics6. Solutions of the transport equations for inhomogeneous thermoelectrics7. Onsager's reciprocal relations in irreversible processesPart II: Quantum theory8. Microscopic description of thermoelectric phenomena9. Calculation of the response to an applied field10. Current density operators for continuous models11. Current density operators for lattice models12. Jonson-Mahan theoremPart III: Comparison of theory and experiment13. Kondo effect in dilute alloys14. Rare earth intermetallics: heavy fermions and valence fluctuators15. First principles approachesAppendix A: Single impurity modelsAppendix B: Green's functionsAppendix C: Derivation of the spectral representation for the single particleAppendix D: Dynamical Mean Field Theory of the PAMAppendix E: ScalingAppendix F: Transport properties of dilute alloysAppendix G: Spectral function in the non-crossing approximation (NCA)Appendix H: Correlation functions in the Fermi liquid regimeAppendix I: Sommerfeld expansion for heavy fermion systems in the DMFT approximation to the periodic Anderson model.