Orbital Inversion and Carrier Confinement in SrTiO$_{3}$/LaAlO$_{3}$ Interfaces Grown on NdGaO$_{3}$ Substrates

We investigate the role of the SrTiO$_{3}$ thickness on the electronic properties of heterointerfaces comprised of NdGaO$_{3}$ (bulk) / SrTiO$_{3}$ (n uc) / LaAlO$_{3}$ (15 uc) using X-ray linear dichroism (XLD) in absorption, Hard X-ray Photoemission Spectroscopy (HAXPES) and DFT$+$U calculations. XLD shows an orbital inversion for \textit{all} STO thicknesses: the lowest energy $d$-orbitals are of \textit{xz/yz} character, unlike `regular' STO/LAO, in which the \textit{xy} orbitals are lowest in energy. For n\textless 6 transport shows the carriers to be localized, HAXPES data showing electronic confinement to the NGO/STO interface. For STO thickness $\ge $8 uc, only weak localization is seen in transport, the STO/LAO interface becomes populated and carrier concentrations approaching half an electron per unit cell are deduced from both Hall measurements and HAXPES. Data from layer-resolved DFT$+$U calculations on STO/LAO and STO/NGO superlattices, and from NGO/STO/LAO are presented and compared to the experimental data, thereby providing a complete picture of the orbital polarization in these systems.