Probing Quantum Confinement and Electronic Structure at Polar Oxide Interfaces.

Polar discontinuities occurring at interfaces between two different materials constitute both a challenge and an opportunity in the study and application of a variety of devices. In order to cure the large electric field occurring in such structures, a reconfiguration of the charge landscape sets in at the interface via chemical modifications, adsorbates or charge transfer. In the latter case, one may expect a local electronic doping of one material: one sparkling example is the two-dimensional electron liquid (2DEL) appearing in SrTiO$_3$ once covered by a polar LaAlO$_3$ layer. Here we show that tuning the formal polarisation of a (La,Al)$_{1-x}$(Sr,Ti)$_x$O$_3$ (LASTO:$x$) overlayer through chemical composition modifies the quantum confinement of the 2DEL in SrTiO$_3$ and its electronic band structure. The analysis of the behaviour in magnetic field of superconducting field-effect devices reveals, in agreement with $ab\ initio$ calculations and self-consistent Poisson-Schr\"odinger modelling, that quantum confinement and energy splitting between electronic bands of different symmetries strongly depend on interface charge densities. These results not only strongly support the polar discontinuity mechanisms with a full charge transfer to explain the origin of the 2DEL at the celebrated LaAlO$_3$/SrTiO$_3$ interface, but also demonstrate an effective tool for tailoring the electronic structure at oxide interfaces.