Topological metal-insulator transition in narrow graphene nanoribbons?

Abstract

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 Lc ≈ 10 nm, where the energy gap drops rather abruptly and topological “end” states appear, linked to dramatically transformed aromaticity. At Lc the conductivity, estimated through an invoked computational scheme, also rises almost discontinuously to a value near the nominal minimum conductivity of grapheneσmin=4e2h. 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 σmin. 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 Lc 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.