which the filled Ti $d$-states extend over $\sim$10 unit cells in the [SrTiO$_3$ ]{}substrate, the only metallic states in the QW systems are localized in the single embedded TiO$_2$ layer, as anticipated.

This new class of quantum wells displays a number of appealing properties that are absent at the LaAlO$_3$/SrTiO$_3$ $n$-type interface. First, the thickness of conduction electrons is controlled by the inserted SrTiO$_3$ film and can be in principle reduced to a single atomic TiO$_2$ layer. Second, the electronic properties of the new quantum wells largely depend on the polar structure of LaAlO$_3$. Therefore, the SrTiO$_3$ substrate can be replaced by other materials on which LaAlO$_3$ can be epitaxially grown, *e.g.* LSAT (La$_{0.29}$Sr$_{0.71}$Al$_{0.65}$Ta$_{0.35}$O$_3$). This provides more choices of substrates on which to grow this new quantum well structure. Finally, the new quantum well serves as a practical way to test the recently proposed hypothesis that some electrons do not contribute to transport due to Anderson localization. Popović *et al.* [@Satpathy-PRL-2008] argued that since all the two dimensional states are Anderson localized by disorder, the electrons that occupy the lowest Ti-$d$ bands do not conduct and therefore the observed sheet carrier density should be much smaller than the 0.5$e$ per 