Mapping the Slow Stabilization of End States with Length along a Laterally Extended Graphene Nanoribbon.

With a lateral bisnaphtho-extended chemical structure, finite 7-13 carbon atom wide armchair graphene nanoribbons (7-13-aGNRs) were on-surface synthesized. For all lengths up to N = 7 monomer units, low-temperature ultrahigh vacuum scanning tunneling spectroscopy and spatial d I /d V maps were recorded at each captured tunneling resonance. The degeneracy of the two central electronic end states (ESs) occurs in a slowly decaying regime with N converging toward zero for N = 6 long 7-13-aGNR (12 bonded anthracenes), while it is N = 2 (4 bonded anthracenes) for seven carbon atoms wide armchair GNRs (7-aGNRs). The two end d I /d V conductance maxima of ESs are also shifted away from strictly two ends of the 7-13-aGNR compared to the 7-aGNR. Using the quantum topology graph filiation between finite length polyacetylene and 7-13-aGNRs wires, we show that this slow decay of 7-13-aGNR ESs is coming from the property of the topological Hückel band matrix that expels the ESs into its eigenvalue spectrum gaps to keep harmony in the core spectrum.