If I may diverge for a moment, Tellurium is an element with a lot of interesting chemistry associated with it. Jim Ibers of Northwestern University wrote an interesting article in Nature Chemistry (2009) about it. It's in the same column as Oxygen and Sulfur on the periodic table, so it shares some aspects the very complicated chemistry that these elements have. However unlike Oxygen and Suflur, it can also form distended Te-Te bonds, in addition to Te-Te single bonds, so oxidation states in metal Telluride compounds are often indeterminate (which sort of implies that Te-containing compounds can have lots of different phases with very different physical and chemical properties).
Tellurium ain't exactly common (it's less abundant than gold, but not in as high demand) nor environmentally benign. Also, thermoelectrics are naturally going to be employed more in high-wear, industrial environments. Furthermore, there is competition for Tellurium from other industries such as thin-film CdTe photovoltaic manufacturers such as First Solar.
Anyway, back to the thermoelectric!
The advance improved ZT, which is the figure of merit for the heat efficiency performance, from about 1.7 to 2.2. ZT governs the Carnot efficiency of the thermoelectric, and hence dictates how close to entropy-limited performance a thermoelectric material can operate. These devices are supposed to operate from a heat source at about 750-900 Kelvin (630 - 480 °C) and dump into room temperature. This is not low-quality heat by any means, as its easily hot enough to make steam, so there's no magic when it comes to thermoelectrics. They still obey the laws of thermodynamics.
The basic trick here is the governing equation,
ZT = σS2/(κel + κlat)from which we see that if you decrease the thermal conductivity, κ, you can improve the performance (electrical conductivity is σ). Thermal energy in solids is primarily conducted by phonons, which are quantized lattice vibrations (i.e. sound). Electrons carry some thermal energy as well, but at the temperature we're concerned with, it's precious little. In order to decrease the thermal conductivity, but not overly decrease the electronic conductivity, you need some structures that are phonon-sized (many atoms). Phonons have a large range of possible wavelengths, so in order to inhibit thermal conductivity you want to provide all wavelengths with something to reflect and scatter from. Hence, the desire is to have a material that is structured/disordered on all potential length scales so there's no window for phonon-driven thermal conductivity to occur in.
The previous body of research, that improved the ZT up to 1.7 involved nanopatterning the thermoelectric with precipitates about 5 nm in diameter. In comparison the microscale crystallites have a much broader distribution of grain sizes, but average around 1 μm (or 1000 nm). The histograms in Figure 3 tell the story.
One concern I would pose is whether the nanostructures and microstructures are stable long-term at the given operating temperature.The melting point of PbTe is 924° C, but the constituents melt at much lower temperatures, so there is the potential for annealing over time.