At interfaces between insulating oxides LaAlO$_3$ and SrTiO$_3$, a two dimensional electron gas (2DEG) has been observed and well studied, while the predicted hole gas (2DHG) has not been realized due to the strong tendency of holes in oxygen $2p$ orbitals to localize. Here we propose, via ab initio calculations, an unexplored class of materials for the realization of parallel two dimensional (2D), two carrier (electron+hole) gases: nitride-oxide heterostructures, with (111)-oriented ScN and MgO as the specific example. Beyond a critical thickness of five ScN layers, this interface hosts spatially separated conducting Sc-$3d$ electrons and N-$2p$ holes, each confined to $sim$two atomic layers -- the transition metal nitride provides both gases. A guiding concept is that the N$^{3-}$ anion should promote robust two carrier 2D hole conduction compared to that of O$^{2-}$; metal mononitrides are mostly metallic and even superconducting while most metal monoxides are insulating. A second positive factor is that the density of transition metal ions, hence of a resulting 2DG, is about three times larger for a rocksalt (111) interface than for a perovskite(001) interface. Our results, including calculation of Hall coefficient and thermopower for each conducting layer separately, provide guidance for new exploration, both experimental and theoretical, on nitride-based conducting gases that should promote study of long sought exotic states viz. new excitonic phases and distinct, nanoscale parallel superconducting nanolayers.
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