Critical thickness for the two-dimensional electron gas in LaTiO3/SrTiO3superlattices

Abstract

Transport dimensionality of Ti $d$ electrons in (LaTiO${}_{3}$)${}_{1}$/(SrTiO${}_{3}$)${}_{N}$ superlattices has been investigated using density functional theory with local spin-density approximation + $U$ method. Different spatial distribution patterns have been found between Ti ${t}_{2g}$ orbital electrons. The ${d}_{xy}$ orbital electrons are highly localized near interfaces due to the potentials by positively charged LaO layers, while the degenerate ${d}_{yz}$ and ${d}_{xz}$ orbital electrons are more distributed inside SrTiO${}_{3}$ insulators. For $N$ \ensuremath{\ge} 3 unit cells (u.c.), the Ti ${d}_{xy}$ densities of state exhibit the staircaselike increments, which appear at the same energy levels as the ${d}_{xy}$ flat bands along the \ensuremath{\Gamma}-$Z$ direction in band structures. The ${k}_{z}$-independent discrete energy levels indicate that the electrons in ${d}_{xy}$ flat bands are two-dimensional electron gases (2DEGs) which can transport along interfaces, but they cannot transport perpendicularly to interfaces due to the confinements in the potential wells by LaO layers. Unlike the ${d}_{xy}$ orbital electrons, the ${d}_{yz}$ and ${d}_{xz}$ orbital electrons have three-dimensional (3D) transport characteristics, regardless of SrTiO${}_{3}$ thicknesses. The 2DEG formation by ${d}_{xy}$ orbital electrons, when $N$ \ensuremath{\ge} 3 u.c., indicates the existence of critical SrTiO${}_{3}$ thickness where the electron transport dimensionality starts to change from 3D to 2D in (LaTiO${}_{3}$)${}_{1}$/(SrTiO${}_{3}$)${}_{N}$ superlattices.