Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mn>2</mn> </msub> </math> Invariants, and Junction States.

Abstract

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 <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mn>2</mn> </msub> </math> 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.