Quantum Confinement at Polar Oxide Interfaces

The discovery of a two-dimensional electron liquid (2DEL), confined at the interface between the two band insulators LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) has generated tremendous research interest. The 2DEL confinement lifts the degeneracy of Ti $t_{2g}$ orbitals and promotes exotic physical properties. A previous study [1] has demonstrated that a 2DEL is also observed when LAO is alloyed with STO (La,Al)$_{1-x}$(Sr,Ti)$_x$O$_3$ (LASTO:$x$). The threshold thickness required for the onset of conductivity scales with $x$. We present here a study of superconductivity at the (LASTO:0.5)/STO interface. The thickness of the 2DEL, measured using perpendicular and parallel critical fields, is larger than the one at the LAO/STO interface. This change is due to a modification on the confining potential linked to a reduced charge transfer that is scaling as $1/x$. This scenario is also confirmed by a self-consistent Poisson-Schrödinger model and ab initio calculations. These compelling evidences support an intrinsic origin to the formation of the 2DEL in the LAO/STO system. \\ [1] M.L. Reinle-Schmitt, et al., Nature Commun. 3, 932 (2012).