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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 possessdistinct 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 electronicproperties can be rationally controlled by bottom-up synthesis from precursormolecules. We derive the value of the topological invariant of the differenttypes of cove-edged and chevron GNRs, and we investigate the electronicproperties of various junctions formed by these GNRs, as well as such GNRs withthe more common armchair or zigzag GNRs. We study the topological junctionstates at the interface of two topologically distinct segments. For an isolatedGNR having two ends of different terminations, topological end states are shownto develop only at the topologically nontrivial end. Our work extends theexplicit categorization of topological invariants of GNRs beyond the previouslydemonstrated armchair GNRs and provides new design rules for novel GNRjunctions as well as future GNR-based nanoelectronic devices.

Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z2 Invariants, and Junction States