  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.

Strongly Correlated Electrons