Topological Metal-Insulator Transition in Narrow Graphene Nanoribbons?

We show that very narrow armchair graphene nanoribbons (AGNRs) of length L and width of 2 zigzag-rings undergo a metal-insulator-like transition at a critical length of 10nm, where the energy gap drops rather abruptly, and the conductivity, estimated, through an invoked computational scheme, rises almost discontinuously to a value between that of a perfect quasi one-dimensional system, and the nominal minimum conductivity of graphene. At this length, the aromatic and non-aromatic rings are interchanged, and sharp peaks appear in the density of states around the Fermi level, suggesting metallic-like behaviour. Such peaks linked to edge states at the Dirac point(s) coincide with the charge-neutrality point(s), associated with the minimum conductivity of graphene. Thus, we have an uncommon combination of interrelated “short-long”, “core-edge,” topological-aromatic transition(s) due to strong quantum confinement, driven by inversion symmetry conflict. The bandgap decreases with the 2/3 power of length before the “transition” and logarithmically afterwards. These effects are practically non-existent for wider AGNRs