  We discovered that La-doped BaSnO3 with the perovskite structure has an
unprecedentedly high mobility at room temperature while retaining its optical
transparency. In single crystals, the mobility reached 320 cm^2(Vs)^-1 at a
doping level of 8x10^19 cm^-3, constituting the highest value among
wide-band-gap semiconductors. In epitaxial films, the maximum mobility was 70
cm^2(Vs)^-1 at a doping level of 4.4x10^20 cm^-3. We also show that resistance
of (Ba,La)SnO3 changes little even after a thermal cycle to 530 Deg. C in air,
pointing to an unusual stability of oxygen atoms and great potential for
realizing transparent high-frequency, high-power functional devices.
