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Books > Science & Mathematics > Physics > States of matter > Condensed matter physics (liquids & solids)
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Modern Theory of Thermoelectricity (Hardcover)
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Modern Theory of Thermoelectricity (Hardcover)
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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 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.
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