Electronic fitness function for screening semiconductors as thermoelectric materials

We introduce a simple but efficient electronic fitness function (EFF) that describes the electronic aspect of the thermoelectric performance. This EFF finds materials that overcome the inverse relationship between $\sigma$ and $S$ based on the complexity of the electronic structures regardless of specific origin (e.g., isosurface corrugation, valley degeneracy, heavy-light bands mixture, valley anisotropy or reduced dimensionality). This function is well suited for application in high throughput screening. We applied this function to 75 different thermoelectric and potential thermoelectric materials including full- and half-Heuslers, binary semiconductors and Zintl phases. We find an efficient screening using this transport function. The EFF identifies known high performance $p$- and $n$-type Zintl phases and half-Heuslers. In addition, we find some previously unstudied phases with superior EFF.