Topological metal-insulator transition in narrow graphene nanoribbons?

We show that very narrow armchair graphene nanoribbons of length L and width of 2 zigzag-rings undergo a metal-insulator-like transition at a critical length L-c approximate to 10 nm, where the energy gap drops rather abruptly and topological "end" states appear, linked to dramatically transformed aromaticity. At L-c the conductivity, estimated through an invoked computational scheme, also rises almost discontinuously to a value near the nominal minimum conductivity of graphene sigma(min) = 4 e(2)/h. The end states (at the zigzag edges) generate sharp peaks in the density of states around the Fermi level at the Dirac points, coinciding with charge-neutrality points, associated with sigma(min). This suggests metallic-like behaviour, which however is an uncommon combination of interrelated "short-long", (or "bulk"-"edge") topological-aromatic transition(s) due to strong quantum confinement, combined with inversion symmetry conflict. This "multi-transition" is rather universal occurring also for wider AGNRs but for a much smaller L-c and in a less sharp way. The assumed lower total energy of such open states is an artefact of the mean-field treatment of the electron-electron interaction. In contrast, the topological "end" states reported here are unique and not spin, but rather pseudospin polarized. Thus, any observed magnetism should be considered non-conventional or of questionable origin. (C) 2021 Elsevier Ltd. All rights reserved.