  We perform a comparative study on thermoelectric performance of
antiperovskite oxides $Ae_3Tt$O and nitrides $Ae_3Pn$N ($Ae=$ Ca, Sr, Ba; $Tt=$
Ge, Sn, Pb; $Pn=$ As, Sb, Bi) by means of first-principles calculation. As for
the oxides with the cubic structure, Ca$_3$GeO with a sizable band gap exhibits
high thermoelectric performance at high temperatures, while Ba$_3$PbO with
Dirac cones without the gap is favorable at low temperatures. The latter high
performance owes to high valley degeneracy including the multiple Dirac cones
and the valleys near the $\Gamma$ and R points. For the nitrides with the cubic
structure, insulator with strong quasi-one-dimensionality exhibits high
thermoelectric performance. We also find that the orthorhombic structural
distortion sometimes sizably enhances thermoelectric performance, especially
for Ba$_3$GeO and Sr$_3$AsN where the high valley degeneracy is realized in the
$Pnma$ phase. Our calculation reveals that antioerpvskites offer a fertile
playground of various kinds of characteristic electronic structure, which
enhance the thermoelectric performance, and provides promising candidates of
high-performance thermoelectric materials.
