  The coupling of optical and electronic degrees of freedom together with
quantum confinement in low-dimensional electron systems is particularly
interesting for achieving exotic functionalities in strongly correlated oxide
electronics. Recently, high room-temperature mobility has been achieved for a
large bandgap transparent oxide - BaSnO$_3$ upon extrinsic La or Sb doping,
which has excited significant research attention. In this work, we report the
observation of room-temperature ferromagnetism in BaSnO$_3$ thin films and the
realization of a two-dimensional electron gas (2DEG) on the surface of
transparent BaSnO$_3$ via oxygen vacancy creation, which exhibits a high
carrier density of $\sim 7.72*10^{14} /{\rm cm}^2$ and a high room-temperature
mobility of ~18 cm$^2$/V/s. Such a 2DEG is rather sensitive to strain and a
less than 0.1% in-plane biaxial compressive strain leads to a giant resistance
enhancement of 350% (more than 540 kOhm/Square) at room temperature. Thus, this
work creates a new path to exploring the physics of low-dimensional oxide
electronics and devices applicable at room temperature.
