Spontaneous 2-Dimensional Carrier Confinement at then-TypeSrTiO3/LaAlO3Interface

Abstract

We describe the intrinsic mechanism of 2-dimensional electron confinement at the $n$-type ${\mathrm{SrTiO}}_{3}/{\mathrm{LaAlO}}_{3}$ interface as a function of the sheet carrier density ${n}_{s}$ via advanced first-principles calculations. Electrons localize spontaneously in Ti $3{d}_{xy}$ levels within a thin ($\ensuremath{\lesssim}2\text{ }\text{ }\mathrm{nm}$) interface-adjacent ${\mathrm{SrTiO}}_{3}$ region for ${n}_{s}$ lower than a threshold value ${n}_{c}\ensuremath{\sim}{10}^{14}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$. For ${n}_{s}>{n}_{c}$ a portion of charge flows into Ti $3{d}_{xz}\mathrm{\text{\ensuremath{-}}}{d}_{yz}$ levels extending farther from the interface. This intrinsic confinement can be attributed to the interface-induced symmetry breaking and localized nature of Ti $3d$ ${t}_{2g}$ states. The sheet carrier density directly controls the binding energy and the spatial extension of the conductive region. A direct, quantitative relation of these quantities with ${n}_{s}$ is provided.