Unusual constructive quantum interference in isolated armchair graphene nanoribbons

Abstract

A new and unusual type of Constructive Quantum Interference (CQI) is revealed in selected isolated armchair graphene nanoribbons (AGNRs). CQI, normally encountered in molecular junctions, occurs when two nearly isoenergetic states interfere constructively. Such almost isoenergetic states are identified here as the energy differences between two pairs of topological end states developed in “wider” AGNRs, through topological metal-insulator-like phase transition, which for 13-AGNRS occurs at a critical length L c ≈ 50 Å. At L c a sudden jump in conductivity by a factor ∼2.5 occurs, which persists up to L ≈ 80 Å and is interpreted as a signature of CQI. Such unusual CQI, in which the zigzag region effectively plays the role of “linkers”, is unique for 13-AGNRs. This is due to their aromaticity i.e., resonance between two different aromatic Clar-sextets, and the resulting symmetry and energy separation of the frontier orbitals. The experimental measurements for 13-AGNRs fully support our results. At a critical length L c a multidimensional phase transition occurs in 13-AGNRs associated with two pairs of nearly isoenergetic end-states and discontinuities in bandgaps and conductivity, which suddenly rises by a factor of ~2.5, signifying a region of constructive quantum interference (CQI). • In wider graphene nanoribbons more than one pair of topological end states occur • These end states appear at critical length L c as metal-insulator phase transitions • For 13-armchair nanoribbons only, this leads to constructive quantum interference • Which is ultimately due to resonance between two aromatic Clar sextets • The role of “linkers” is played by the zigzag ends where end-states are localized