Thermoelectricity near Anderson localization transitions

Kaoru Yamamoto*, Amnon Aharony, Ora Entin-Wohlman, Naomichi Hatano

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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 us to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at nonzero 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 nonuniversal 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. USA 93, 7436 (1996)PNASA60027-842410.1073/pnas.93.15.7436] for a narrow energy range of the zero-temperature metallic behavior.

Original languageEnglish
Article number155201
JournalPhysical Review B
Issue number15
StatePublished - 5 Oct 2017


FundersFunder number
Ministry of Science and Technology
UCLA Chicano Studies Research Center
Japan Society for the Promotion of Science15K05207, 16J11542, 15K05200, 26400409
Israel Science Foundation
University of Tokyo
Ministry of Science and Technology, Israel3-11173


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