  LaOBiPbS$_3$ is a kind of pnictogen-dichalcogenide layered compounds, which
have recently been experimentally investigated as thermoelectric materials
owing to their low thermal conductivity and high controllability of constituent
elements. However, thermoelectric performance of LaOBiPbS$_3$ is at present not
very high and that of its analogous compounds remains to be unknown. In this
study, we theoretically investigate thermoelectric properties of 24 possible
variations of the constituent elements in LaOBiPbS$_3$ from the viewpoint of
the electronic structure. We find that some compounds can have much better
thermoelectric performance than LaOBiPbS$_3$; in particular, LaOSbPbSe$_3$ is
predicted to have a power factor five times as large as that of LaOBiPbS$_3$.
Here, the choice of the pnictogen atom (As, Sb, and Bi), of which the
low-energy conduction bands mainly consist, correlates with the calculated
power factor and the dimensionless figure of merit, $ZT$. Such correlation
comes from the fact that the low-dimensionality of the electronic structure,
which enhances the density of states near the band edge, strongly depends on
the pnictogen atom through, e.g., the strength of the spin-orbit coupling.
Moreover, hybridization of the wave functions in the pnictogen-dichalcogenide
layer and those in the rock-salt layer plays a key role in gap opening, and
thus is important for achieving high thermoelectric performance. In
LaOSbPbSe$_3$, such hybridization also pushes up the conduction band bottom,
which enhances the density of states near the band edge and thus the power
factor.
