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Most recently, orbital-selective quantum well states of $d$ electrons havebeen experimentally observed in SrVO$_3$ ultrathin films [K. Yoshimatsu et.al., Science 333, 319 (2011)] and SrTiO$_3$ surfaces [A. F. Santander-Syro et.al., Nature 469, 189 (2011)]. Hitherto, one tries to explain these experimentsby a nearly free electron (NFE) model, an approach widely used for delocalizedelectrons in semiconductor heterostructures and simple metal films. We showthat a tight binding (TB) model is more suitable for describingheterostructures with more localized $d$ electrons. In this paper, we constructfrom first principles simple TB models for perovskite oxide heterostructuresand surfaces. We show that the TB model provides a simple intuitive physicalpicture and yields, already with only two parameters, quantitatively much morereliable results, consistent with experiment.

Quantum confinement in perovskite oxide heterostructures: tight binding instead of nearly free electron picture