Lattice screening of the polar catastrophe in KNbO$_{3}$/BaTiO$_{3}$ interfaces

The discovery of a bidimensional electron gas (2DEG) in the interface between two insulating lattices like LaAlO$_3$ and SrTiO$_3$ has triggered much interest around bidimensional conductivity in these heterostructures. In this work we study polar interfaces between KNbO$_{3}$ (KNO) and BaTiO$_{3}$ (BTO), equivalent from the layer by layer charge point of view to the LAO/STO. In particular we focus on: (a) the possibility of formation of a 2DEG, (b) its interaction with the ferroelectric distortions of these materials, and (c) the effect of external electric fields. For this, we have performed Density Functional Theory calculations for a KNO($m$)/BTO(2$m$)/KNO($m$) slab ($m$= width in unit cells) with different kinds of interfaces ($n$ or $p$). We find that a 2DEG is formed only in the unrelaxed configuration, where there is no rumpling between the atoms of a given layer. However, when geometry is relaxed, KNbO$_{3}$ polarizes and the 2DEG is effectively screened. This effect is robust even under application of electric fields of moderate size. Finally, we find that an easily-rotated [110] in-plane polarization, driven by electrostatic effects, appears in the vicinity of the KO/TiO$_2$-type interface even thought the system is under in-plane compressive strain.