two-dimensional unit cell predicted by the polar catastrophe mechanism [@Hwang-NatMat-2006]. Nevertheless, it is not trivial to distinguish from which band conduction electrons originate. The thinnest of this new type of quantum wells has only one Ti-$d$ band at the Fermi level, corresponding to the single embedded TiO$_2$ layer, which has a strong two-dimensional Ti-$d_{xy}$ character. Therefore it should show strong localization and not contribute to conductivity. By thickening the embedded SrTiO$_3$, one should be changing only the extent of the wave functions and see the localization properties. Fig. \[fig:bands\_compare\] shows a comparison of the band structures of the $n$-type interface and the QW. These two systems both have approximately 0.1$e$ per two-dimensional unit cell (from Fig. \[fig:charge\]). However, the Fermi level of the $n$-type interface crosses three Ti-$d$ bands, while the QW system has only one Ti-$d$ band at the Fermi level, as expected.

![\[fig:bands\_compare\] A comparison of the band structures of [**a)**]{} the $n$-type interface and [**b)**]{} the new QW. The $n$-type interface has 5 unit cells of LaAlO$_3$ and the QW has a capping layer of 6 unit cells of LaAlO$_3$. The red solid line is the Fermi level.](bands_compare.ps){width="16cm"}

          $np$-type                         $n$-type                         $p$-type                            QW       
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