conductivity, the majority of these materials are explored in the context of nanostructuring. Many approaches towards this route are common practice, such as superlattice-like geometries [@Mizuno15], alloying [@XWWang08], heavy doping [@Ikeda10], nanoporous materials [@Verdier16; @RYang05; @JHLee08], nanograining [@Neo13ntech; @Bennett16], nanoinclusions (NIs) [@Biswas12; @Gayner16; @Zou15; @Hopkins11; @Vineis10; @Popescu09], etc. Nanoinclusions, in particular, cause scattering of short wavelength phonons with mean-free-paths in the order of nanometers, which otherwise contribute significantly in the thermal conductivity of common TE materials, such as in PbTe [@Bo11]. This technique is applied to a broad range of materials, including Bi$_2$Te$_3$ [@Fan11; @Keshavarz14], PbTe [@Heremans05; @Biswas12; @Hsu04], SiGe [@Ahmad16; @XWWang08; @Zhu09], MnSi [@Saleemi15], and SnTe [@Tan14], to name a few.

Furthermore, undoubtedly, one of the most successful approaches to reduce thermal conductivity is hierarchical nanostructuring, where distortion features are placed within a matrix material at the mesoscale (grains/boundaries), microscale (NIs) and nanoscale (atomic defects). These scatter phonons of various wavelengths and reduce phonon transport across the entire spectrum. Indeed, by nanostructuring PbTe in a hierarchical manner, record high value of $ZT=2.2$ was achieved due to drastic reductions in $\kappa_\ell$ [@Biswas12]. More recent works have achieved even higher $ZT$ up to $2.5$ at $923$ K [@GTan16]. For such a 