The Importance of Avoided Crossings in Understanding High Valley Degeneracy in Half-Heusler Thermoelectric Semiconductors

Half-Heusler (hH) compounds are promising candidates for inexpensive, low-toxicity thermoelectric materials. It is well known that engineering electronic bands with high valley degeneracy is an effective approach for enhancing the performance of thermoelectric materials, and there are several routes for achieving high valley degeneracy in hH systems. For instance, there are multiple locations in the first Brillouin zone where the valence band maximum can be found (at the Γ-, L-, or W-point), and there are two competing low-lying conduction bands at the X-point, where the conduction band minimum is located. By converging the multiple valence band and conduction band extrema, the valley degeneracy, and hence, performance of these materials can be improved. Here, group theoretical and tight-binding approaches, in addition to first-principles density functional theory calculations, are used to study the chemical origins of various band extrema in both the n-type and p-type compounds, with particular focus on ZrNiSn and NbFeSb. Specifically, the importance of avoided crossings is explained. The results of this work can be used to better understand and develop design strategies for engineering better performing hH thermoelectrics.