  The field of thermoelectric materials has undergone a revolutionary
transformation over the last couple of decades as a result of the ability to
nanostructure and synthesize myriads of materials and their alloys. The ZT
figure of merit, which quantifies the performance of a thermoelectric material
has more than doubled after decades of inactivity, reaching values larger than
two, consistently across materials and temperatures. Central to this ZT
improvement is the drastic reduction in the material thermal conductivity due
to the scattering of phonons on the numerous interfaces, boundaries,
dislocations, point defects, phases, etc., which are purposely included. In
these new generation of nanostructured materials, phonon scattering centers of
different sizes and geometrical configurations (atomic, nano- and macro-scale)
are formed, which are able to scatter phonons of mean-free-paths across the
spectrum. Beyond thermal conductivity reductions, ideas are beginning to emerge
on how to use similar hierarchical nanostructuring to achieve power factor
improvements. Ways that relax the adverse interdependence of the electrical
conductivity and Seebeck coefficient are targeted, which allows power factor
improvements. For this, elegant designs are required, that utilize for instance
non-uniformities in the underlying nanostructured geometry, non-uniformities in
the dopant distribution, or potential barriers that form at boundaries between
materials. A few recent reports, both theoretical and experimental, indicate
that extremely high power factor values can be achieved, even for the same
geometries that also provide ultra-low thermal conductivities. Despite the
experimental complications that can arise in having the required control in
nanostructure realization, in this colloquium, we aim to demonstrate, mostly
theoretically, that it is a very promising path worth exploring.
