Critical thickness for the two-dimensional electron gas in LaTiO3/SrTiO3 superlattices

Transport dimensionality of Ti d electrons in (LaTiO3)(1)/(SrTiO3)(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 SrTiO3 insulators. For N >= 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 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 SrTiO3 thicknesses. The 2DEG formation by d(xy) orbital electrons, when N >= 3 u.c., indicates the existence of critical SrTiO3 thickness where the electron transport dimensionality starts to change from 3D to 2D in (LaTiO3)(1)/(SrTiO3)(N) superlattices.