Peculiar electronic properties of wider armchair graphene nanoribbons: Multiple topological end-states and “phase transitions”

Abstract

In contrast to the thinner 5,6,7-AGNRs in which one pair of topological end-states is generated at a critical length Lc in a form of a metal-insulator-like “phase transition”, in wider AGNRs (with Z = 3n, 3n±1, n = ,2, 3 … zigzag rings) n ≥ 2 pairs of end-states (associated with n ≥ 2 transitions) can be produced, with very peculiar properties, such as quantum interference (QI), stemming from the interaction between (multiple) pairs of end states localized in the same narrow region. At the level of density functional theory such AGNRs at large enough lengths would be misleadingly appear as highly spin polarized with spin s = n. Our results are fully supported by experiment, wherever available. We verify that the Z = 3n-1 AGNRs are always metallic with near zero bandgap, as was originally believed, contrary to some recent suggestions, and do not strictly follow the above pattern. It is shown that in the 13-AGNRs (Z = 3n, n = 2) a unique and intense (close to the theoretical limit) constructive QI (CQI) appears, which covers a relatively wide region of lengths from about L∼ 50 Å to L∼80 Å. This peculiar L-dependent CQI is strongly related to their aromaticity pattern consisting of migrating Clar sextets. The rest of AGNRs exhibit only small kinks (for n = 2) or dips (for n = 3) in conductivity, which could be considered as weak and narrow CQI, or DQI (destructive QI), respectively.