  Zintl compounds have been extensively studied for their outstanding
thermoelectric properties, but their electronic structure remains largely
unexplored. Here, we present a detailed investigation of the electronic
structure of the isostructural thermopower materials YbMg$_2$Bi$_2$ and
CaMg$_2$Bi$_2$ using angle-resolved photoemission spectroscopy (ARPES) and
density functional theory (DFT). The ARPES results show a significantly smaller
Fermi surface and Fermi velocity in CaMg$_2$Bi$_2$ than in YbMg$_2$Bi$_2$. Our
ARPES results also reveal that in the case of YbMg$_2$Bi$_2$, Yb-4$f$ states
reside well below the Fermi level and likely have a negligible impact on
transport properties. To properly model the position of 4$f$-states, as well as
the overall electronic structure, a Hubbard $U$ at the Yb sites and spin-orbit
coupling (SOC) have to be included in the DFT calculations. Interestingly, the
theoretical results reveal that both materials belong to a $Z_2$ topological
class and host robust topological surface states around $E_\mathrm {F}$. Due to
the intrinsic hole doping, the topological states reside above the Fermi level,
inaccessible by ARPES. Our results also suggest that in addition to SOC,
vacancies and the resulting hole doping play an important role in the transport
properties of these materials.
