Band Inversion-Driven High Valley Degeneracy

Thermoelectric materials can convert thermal energy to electrical energy and vice versa, enabling low-carbon alternatives for cooling and waste heat recovery. Yet, the low power conversion efficiencies of existing thermoelectric materials remain a challenge. One method to improve the thermoelectric performance of a material is by tuning the valley degeneracy, which we can control by modifying the degree to which the bands are inverted. We generalize this concept of “band inversion-driven high valley degeneracy” and derive simple rules for when inverted-band materials exhibit high thermoelectric performance. Using a combination of <i>k.p</i> perturbation theory and Density Functional Theory calculations, we show that electronic bands must be inverted to a critical degree for a material to possess high valley degeneracy. We apply this rule to discover potentially high-performing thermoelectric materials within the <i>ABX </i>chemical space of materials. We find that NaCaBi (space group: <i>P6₃/mmc</i>) is a promising candidate with a degeneracy of 6 for both the conduction and valence bands, resulting from the high degree of band inversion in the material. Through detailed Boltzmann transport theory-based calculations, we find that NaCaBi can reach <i>zT</i> between 0.4 and 0.8 at 300 K. Our study therefore demonstrates that band inversion is a rational descriptor for identifying high-performing thermoelectric materials.