  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.
