  Quasi-two-dimensional electron systems (q-2DES) are formed in various
hetero-structures, including oxide interfaces. Oxygen vacancies (OVs) in oxides
like $\mathrm{SrTiO_3}$ are known to produce electronic carriers. A novel way
to produce $\mathrm{SrTiO_{3-\delta}}$ on the surface using a low-energy
$\mathrm{H_2}$ plasma is shown here. It results in a q-2DES with mobility as
high as $\mu \sim 20,000 \; cm^2V^{-1}s^{-1}$, displaying quantum oscillations
in magneto-resistance. We can achieve a sharper or weaker confinement potential
by adjusting the process pressure. The system with sharper confinement displays
clearer quantum oscillations and Kondo-like temperature dependence of
resistance. OVs close to the surface behaving like a correlated Anderson
impurity is responsible for the Kondo behaviour. Quantum oscillations are less
prominent in the weakly confined system. A cross-over from weak-localization to
anti-localization with temperature is seen, but no Kondo behavior. The process
also results in a transparent conductor amenable to lithographic patterning.
This conductor's standard figure of merit is comparable to poly-crystalline ITO
films in the visible regime and extends with similar performance into the
$\lambda$ $\sim 1.5$ $\mu m$ telecommunication wavelength.
