Signature of band inversion in the perovskite thin-film alloys BaSn$_{1-x}$Pb$_x$O$_3$

Perovskite oxides ABO$_3$ containing heavy B-site elements are a class of candidate materials to host topological metals with a large spin-orbit interaction. In contrast to the band insulator BaSnO$_3$, the semimetal BaPbO$_3$ is proposed to be a typical example with an inverted band structure, the conduction band of which is composed of mainly the O-2p orbital. In this study, we exemplify a band-gap modification by systematic structural, optical, and transport measurements in BaSn$_{1-x}$Pb$_x$O$_3$ films. A sudden suppression of the conductivity and an enhancement of the weak antilocalization effect at $x$ = 0.9 indicate the presence of a singular point in the electronic structure as a signature of the band inversion. Our findings provide an intriguing platform for combining topological aspects and electron correlation in perovskite oxides based on band-gap engineering.