We show that the spin-Hall conductivity in insulators is related to a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin-Hall effect. As a result, we theoretically predict that two-dimensional bismuth will show the quantum spin-Hall effect, both by calculating the helical edge states, and by showing the nontriviality of the ${Z}_{2}$ topological number, and propose possible experiments.

https://arxiv.org/pdf/cond-mat/0607001.pdf

Quantum spin Hall effect and enhanced magnetic response by spin-orbit coupling.

Recent advances in thermoelectric materials

Thermoelectric materials can be used for solid state power generation and heating/cooling applications. The figure of merit of thermoelectric materials, ZT, which determines their efficiency in a thermoelectric device, remains low for most conventional bulk materials. Nanoscale and nanostructured thermoelectric materials are promising for increasing ZT relative to the bulk. This review introduces the theory behind thermoelectric materials and details the predicted and demonstrated enhancements of ZT in nanoscale and nanostructured thermoelectric materials. We discuss thin films and superlattices, nanowires and nanotubes, and nanocomposites, providing a ZT comparison among various families of nanocomposite materials. We provide some perspectives regarding the origin of enhanced ZT in nanoscale and nanostructured materials and suggest some promising and fruitful research directions for achieving high ZT materials for practical applications.

Enhancement of the thermoelectric properties in nanoscale and nanostructured materials

We examine the effect of strong three-dimensional quantum confinement on the thermopower and electrical conductivity of PbSe nanocrystal superlattices. We show that for comparable carrier concentrations PbSe nanocrystal superlattices exhibit a substantial thermopower enhancement of several hundred microvolts per Kelvin relative to bulk PbSe. We also find that thermopower increases monotonically as the nanocrystal size decreases due to changes in carrier concentration. Lastly, we demonstrate that thermopower of PbSe nanocrystal solids can be tailored by charge-transfer doping.

http://wang.faculty.asu.edu/wp-content/uploads/2012/02/Wang-2008-Enhanced-thermopwer-in-PbSe-NC-QD-superlattices.pdf

Enhanced thermopower in PbSe nanocrystal quantum dot superlattices.

Langmuir-Blodgett films

In PbSe epitaxial thin films grown by thermal evaporation on KCl(001) substrates and covered with an EuS protective layer, oscillatory dependences of the galvanomagnetic and thermoelectric properties (electrical conductivity σ, the Hall coefficient RH, charge carrier mobility μ, and the Seebeck coefficient S) on the PbSe layer thickness d (3<d<200 nm) were observed at room temperature. Oscillations of the transport properties are associated with quantum size effects due to electron confinement in the PbSe quantum wells.

Quantum size effects in PbSe quantum wells

We report on the thickness d dependences of the Seebeck coefficient, electrical conductivity, and Hall coefficient of PbTe and PbS epitaxial thin films (d=5–200 nm), prepared by thermal evaporation in vacuum and deposition on (001) KCl substrates. The oxidation of the films in air at 300 K leads to a sign inversion of the carrier type from n to p in films with d⩽125 and 110 nm for PbTe and PbS, respectively. The observed d dependences are interpreted in terms of compensating acceptor states created by oxygen on the film surface.

Effect of oxidation on the thermoelectric properties of PbTe and PbS epitaxial films

Oscillatory thickness dependences of the electrical conductivity, Hall coefficient, charge carrier mobility, and Seebeck coefficient were obtained at room temperature for n-type thin Bi films (d=3–300 nm) fabricated by the thermal evaporation of a bismuth crystal in a vacuum and deposition on mica substrates at 380 K. We attribute this oscillatory behavior to quantum-size effects, which are observable when the electron mean-free path and Fermi wave length exceed the film thickness d.

Quantum-size effects in n-type bismuth thin films

Oscillatory behaviour was detected in the dependences of the transport properties (electrical conductivity, Hall coefficient, charge carrier mobility, Seebeck coefficient and thermoelectric power factor) on the PbTe layer thickness d (d = 2–200 nm) in (001) KCl/PbTe/EuS quantum well (QW) structures at room temperature. The non-monotonic character of these dependences is attributed to quantum size effects, which manifest themselves in PbTe QWs at sufficiently small values of d. The positions of the extrema in the thickness dependences of the transport properties shift with changing electron concentration in PbTe QWs.

https://iopscience.iop.org/article/10.1088/0957-4484/14/1/313/pdf

M. S. Dresselhaus

Papers

Quantum size effects in PbSe quantum wells

Effect of oxidation on the thermoelectric properties of PbTe and PbS epitaxial films

Quantum-size effects in n-type bismuth thin films

Oscillatory behaviour of the transport properties in PbTe quantum wells

Effect of thickness on the thermoelectric properties of PbS thin films