In cove-edged zigzag graphene nanoribbons (ZGNR-Cs), one terminal CH group per length unit is removed on each zigzag edge, forming a regular pattern of coves that controls their electronic structure. Based on three structural parameters that unambiguously characterize the atomistic structure of ZGNR-Cs, we present a scheme that classifies their electronic state (i.e., if they are metallic, topological insulators, or trivial semiconductors) for all possible widths $N$, unit lengths $a$, and cove position offsets at both edges $b$, thus showing the direct structure-electronic structure relation. We further present an empirical formula to estimate the band gap of the semiconducting ribbons from $N$, $a$, and $b$. Finally, we identify all geometrically possible ribbon terminations and provide rules to construct ZGNR-Cs with a well-defined electronic structure.

• Received 31 May 2022
• Accepted 20 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.216401