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Emergent phases in the two-dimensional electron gas (2DEG) formed at theinterface between two insulating oxides have attracted great attention in thepast decade. We present ab-initio electronic structure calculations for theinterface between a Mott insulator GdTiO$_3$ (GTO) and a band insulatorSrTiO$_3$ (STO) and compare our results with those for the widely studiedLaAlO$_3$/SrTiO$_3$ (LAO/STO) interface between two band insulators. OurGTO/STO results are in excellent agreement with experiments, but qualitativelydifferent from LAO/STO. We find an interface carrier density of 0.5$e^{-}$/Ti,independent of GTO thickness in both superlattice and thin film geometries, incontrast to LAO/STO. The superlattice geometry in LAO/STO offers qualitativelythe same result as in GTO/STO. On the other hand, for a thin film geometry, theinterface carrier density builds up only beyond a threshold thickness of LAO.The positive charge at the vacuum surface that compensates the 2DEG at theinterface also exhibits distinct behaviors in the two systems. The top GTOlayer is found to be insulating due to correlation-driven chargedisproportionation, while the top LAO layer is metallic within band theory andmay become insulating due to surface disorder or surface reconstruction.

Electronic Structure of Oxide Interfaces: A Comparative Analysis of GdTiO$_3$/SrTiO$_3$ and LaAlO$_3$/SrTiO$_3$ Interfaces