Materials and Methods 1. Sample preparation method Tl-doped PbTe was made by direct reaction of appropriate amounts of Pb, Te, and Tl 2 Te in a fused-silica tube sealed under a vacuum. Each sample was briefly melted at 1273 K for 24 h and lightly shaken to ensure homogeneity of the liquid, then furnace cooled to 800 K and annealed for 1 week. The obtained ingot was crushed into fine powder and hot-pressed at 803 K for 2 hours under a flowing 4% H 2-Ar atmosphere. The final form of each polycrystalline sample was a 2mm thick disk about 10 mm in diameter. Phase purity was checked by powder X-ray diffraction. No impurity phases were found in the XRD patterns, indicating that all added Tl was dissolved in PbTe. The purities of all starting materials were at least 99.99%. The samples were stable in air at room temperature.

The past two decades have witnessed the rapid growth of thermoelectric (TE) research. Novel concepts and paradigms are described here that have emerged, targeting superior TE materials and higher TE performance. These superior aspects include band convergence, "phonon-glass electron-crystal", multiscale phonon scattering, resonant states, anharmonicity, etc. Based on these concepts, some new TE materials with distinct features have been identified, including solids with high band degeneracy, with cages in which atoms rattle, with nanostructures at various length scales, etc. In addition, the performance of classical materials has been improved remarkably. However, the figure of merit zT of most TE materials is still lower than 2.0, generally around 1.0, due to interrelated TE properties. In order to realize an "overall zT > 2.0," it is imperative that the interrelated properties are decoupled more thoroughly, or new degrees of freedom are added to the overall optimization problem. The electrical and thermal transport must be synergistically optimized. Here, a detailed discussion about the commonly adopted strategies to optimize individual TE properties is presented. Then, four main compromises between the TE properties are elaborated from the point of view of the underlying mechanisms and decoupling strategies. Finally, some representative systems of synergistic optimization are also presented, which can serve as references for other TE materials. In conclusion, some of the newest ideas for the future are discussed.

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