Efficient thermoelectric materials using nonmagnetic double perovskites with $d^0$/$d^6$ band filling
Efficient thermoelectric materials should present large Seebeck coefficient, high electrical conductivity and low thermal conductivity. An enhanced Seebeck coefficient can be obtained from materials where the Fermi level can be aligned with a large and narrow peak of the density of states, particularly when a substantial band valley degeneracy occurs. A high electrical conductivity comes as a consequence of large conductive hopping paths between the atoms of the material. Both physical quantities can be decoupled and optimized independently if their origins can be ascribed to different sets of bands. Based on these assumptions, double perovskites A$_2$BB'O$_6$ with $d^0/d^6$ filling for the B and B' metal cations, respectively, have been considered. They provide a desirable band structure with degenerate B-$t_{2g}$ / B'-$e_g$ bands above the Fermi level together with a low thermal conductivity. We have carried out first-principles simulations for various of these nonmagnetic double perovskites and showed that all of them present a large Seebeck coefficient (consequence of the localized and empty $t_{2g}$ states of the B-cation), and large electrical conductivity due to the more spread unoccupied $e_{g}$ band of the B' cation. We have seen that if they can be optimally doped, they could show a figure of merit comparable or even higher than the best $n$-type thermoelectric oxides, such as SrTiO$_{3}$. Different mechanisms to tune the band structure and enhance the thermoelectric figure of merit are explored, including epitaxial strain, hydrostatic pressure, chemical pressure, and external doping. A fully relaxed structure has also been studied, showing that a realistic calculation is necessary to make accurate predictions, but also proving that the main trends shown throughout the paper remain unchanged.