  Graphene nanoribbons (GNRs) have recently been shown by Cao, Zhao, and Louie
[Cao, T.; Zhao, F.; Louie, S. G. Phys. Rev. Lett. 2017, 119, 076401] to possess
distinct topological phases in general, characterized by a Z2 invariant.
Cove-edged and chevron GNRs moreover are chemically and structurally diverse,
quasi-one-dimensional (1D) nanostructures whose structure and electronic
properties can be rationally controlled by bottom-up synthesis from precursor
molecules. We derive the value of the topological invariant of the different
types of cove-edged and chevron GNRs, and we investigate the electronic
properties of various junctions formed by these GNRs, as well as such GNRs with
the more common armchair or zigzag GNRs. We study the topological junction
states at the interface of two topologically distinct segments. For an isolated
GNR having two ends of different terminations, topological end states are shown
to develop only at the topologically nontrivial end. Our work extends the
explicit categorization of topological invariants of GNRs beyond the previously
demonstrated armchair GNRs and provides new design rules for novel GNR
junctions as well as future GNR-based nanoelectronic devices.
