  We employ first-principles calculations based density-functional-theory (DFT)
approach to study electronic properties of partially and fully
edge-hydrogenated armchair boron-nitrogen-carbon (BNC) nanoribbons (ABNCNRs),
with widths between 0.85 nm to 2.3 nm. Due to the partial passivation of edges,
electrons which do not participate in the bonding, form new energy states
located near the Fermi-level. Because of these additional bands, some ABNCNRs
exhibit metallic behavior, which is quite uncommon in armchair nanoribbons. Our
calculations reveal that the metallic behavior is observed for the following
passivation patterns: (i) when B atom from one edge, and N atom from another
edge, are unpassivated. (ii) when N atoms from both the edges are unpassivated.
(iii) when C atom from one edge, and N atom from another edge, are
unpassivated. Furthermore, spin-polarization is also observed for certain
passivation schemes, which is also quite uncommon for armchair nanoribbons.
Thus, our results suggest that ABNCNRs exhibit a wide range of electronic and
{magnetic }properties in that the fully edge-hydrogenated ABNCNRs are direct
band gap semiconductors, while partially edge-hydrogenated ones are either
semiconducting, or metallic, while simultaneously exhibiting spin polarization,
based on the nature of passivation. We also find that the ribbons with larger
widths are more stable, as compared to the narrower ones.
