Two-dimensional electron gas in SrTiO$_{3}$

We report on Shubnikov-de Haas (SdH) oscillations in a two-dimensional electron gas (2DEG) in delta-doped SrTiO$_{3}$ thin films. The existence of a 2DEG is confirmed by the angular dependence of the SdH oscillations. The observed SdH oscillation frequency corresponds to a carrier concentration of, which is only 4{\%} of the total Hall carrier density. We show that the only electrons in one of the sub-bands confined by the delta-doping potential have sufficient mobility to exhibit quantum oscillations. Guided by the similarity of the confined $d$-band electron states in SrTiO$_{3}$ to the confined hole systems in conventional semiconductors, quantum oscillations are interpreted in terms of spin and Landau level splitting. Despite the inherent complexity of a sub-band that is derived from four $d$-band states near the conduction band minimum of SrTiO$_{3}$, we show that the quantum oscillations can be modeled quantitatively. Alternative routes to realize high mobility 2DEGs in SrTiO$_{3}$ will also be discussed.