  BaSnO$_3$ exhibits the highest carrier mobility among perovskite oxides,
making it ideal for oxide electronics. Collective charge carrier oscillations,
plasmons, are expected to arise in this material, thus providing a tool to
control the nanoscale optical field for optoelectronics applications. Here, we
demonstrate the existence of relatively long-lived plasmons supported by
high-mobility charge carriers in La-doped BaSnO$_3$ (BLSO). By exploiting the
high spatial and energy resolution of electron energy-loss spectroscopy with a
focused beam in a scanning transmission electron microscope, we systematically
investigate the dispersion, confinement ratio, and damping of infrared
localized surface plasmons (LSP) in BLSO nanoparticles. We find that the LSPs
in BLSO are highly spatially confined compared to those sustained by noble
metals and have relatively low loss and high quality factor compared to other
doped oxides. Further analysis clarifies the relation between plasmon damping
and carrier mobility in BLSO. Our results support the use of nanostructured
degenerate semiconductors for plasmonic applications in the infrared region and
establish a relevant alternative to more traditional plasmonic materials.
