The electronic thermoelectric coefficients are analyzed in the vicinity of
one and two Anderson localization thresholds in three dimensions. For a single
mobility edge, we correct and extend previous studies, and find universal
approximants which allow to deduce the critical exponent for the
zero-temperature conductivity from thermoelectric measurements. In particular,
we find that at non-zero low temperatures the Seebeck coefficient and the
thermoelectric efficiency can be very large on the "insulating" side, for
chemical potentials below the (zero-temperature) localization threshold.
Corrections to the leading power-law singularity in the zero-temperature
conductivity are shown to introduce non-universal temperature-dependent
corrections to the otherwise universal functions which describe the Seebeck
coefficient, the figure of merit and the Wiedemann-Franz ratio. Next, the
thermoelectric coefficients are shown to have interesting dependences on the
system size. While the Seebeck coefficient decreases with decreasing size, the
figure of merit first decreases but then increases, while the Wiedemann-Franz
ratio first increases but then decreases as the size decreases. Small (but
finite) samples may thus have larger thermoelectric efficiencies. In the last
part we study thermoelectricity in systems with a pair of localization edges,
the ubiquitous situation in random systems near the centers of electronic
energy bands. As the disorder increases, the two thresholds approach each
other, and then the Seebeck coefficient and the figure of merit increase
significantly, as expected from the general arguments of Mahan and Sofo [J. D.
Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] for a
narrow energy-range of the zero-temperature metallic behavior.Comment: 16 pages, 11 figures, close to the published versio