The Importance of Avoided Crossings in Understanding Band Convergence in Half-Heusler Thermoelectric Semiconductors

When designing high-performance thermoelectric (TE) semiconductors, it is greatly beneficial to engineer electronic bands that have high valley degeneracy, N_V, or multiple carrier pockets near the transport edge. High N_V can be achieved by having band extrema at low symmetry points in the Brillouin zone (BZ) and by having multiple band extrema converged within a few k_BT. Half-Heusler (hH) compounds comprise a promising class of TEs that benefit from low cost, low toxicity, and high stability. While there are dozens of known base compositions (XYZ) for hH TEs, they can be categorized into just three categories based on the location of the valence band maximum (VBM) in the BZ (at L, W or Γ). Thus, the performance of p-type hH TEs is improved when the lower-symmetry VBMs (L or W) are favored or when two or more of the competing VBMs are converged. While high-throughput density functional theory (DFT) calculations have helped identify chemical trends for predicting the VBM location, there has been no consistent explanation of their origins. In this work, we show that avoided crossings are key to understanding the origins of the three VBMs and their relative energies.  We employ DFT, group theory, and tight binding to describe the interactions responsible for these avoided crossings.