  Recent theoretical studies employing density-functional theory have predicted
BaBiO$_{3}$ (when doped with electrons) and YBiO$_{3}$ to become a topological
insulator (TI) with a large topological gap (~ 0.7 eV). This, together with the
natural stability against surface oxidation, makes the Bismuth-Oxide family of
special interest for possible applications in quantum information and
spintronics. The central question, we study here, is whether the hole-doped
Bismuth Oxides, i.e. Ba$_{1-x}$K$_{x}$BiO$_{3}$ and
BaPb$_{1-x}$Bi$_{x}$O$_{3}$, which are "high-Tc" bulk superconducting near 30
K, additionally display in the further vicinity of their Fermi energy $E_{F}$ a
topological gap with a Dirac-type of topological surface state. Our electronic
structure calculations predict the K-doped family to emerge as a TI, with a
topological gap above $E_{F}$. Thus, these compounds can become superconductors
with hole-doping and potential TIs with additional electron doping.
Furthermore, we predict the Bismuth-Oxide family to contain an additional Dirac
cone below $E_{F}$ for further hole doping, which manifests these systems to be
candidates for both electron- and hole-doped topological insulators.
