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The field of thermoelectric materials has undergone a revolutionarytransformation over the last couple of decades as a result of the ability tonanostructure and synthesize myriads of materials and their alloys. The ZTfigure of merit, which quantifies the performance of a thermoelectric materialhas more than doubled after decades of inactivity, reaching values larger thantwo, consistently across materials and temperatures. Central to this ZTimprovement is the drastic reduction in the material thermal conductivity dueto the scattering of phonons on the numerous interfaces, boundaries,dislocations, point defects, phases, etc., which are purposely included. Inthese new generation of nanostructured materials, phonon scattering centers ofdifferent sizes and geometrical configurations (atomic, nano- and macro-scale)are formed, which are able to scatter phonons of mean-free-paths across thespectrum. Beyond thermal conductivity reductions, ideas are beginning to emergeon how to use similar hierarchical nanostructuring to achieve power factorimprovements. Ways that relax the adverse interdependence of the electricalconductivity and Seebeck coefficient are targeted, which allows power factorimprovements. For this, elegant designs are required, that utilize for instancenon-uniformities in the underlying nanostructured geometry, non-uniformities inthe dopant distribution, or potential barriers that form at boundaries betweenmaterials. A few recent reports, both theoretical and experimental, indicatethat extremely high power factor values can be achieved, even for the samegeometries that also provide ultra-low thermal conductivities. Despite theexperimental complications that can arise in having the required control innanostructure realization, in this colloquium, we aim to demonstrate, mostlytheoretically, that it is a very promising path worth exploring.

Hierarchically nanostructured thermoelectric materials: Challenges and opportunities for improved power factors