  In cove-edged zigzag graphene nanoribbons (ZGNR-C), one terminal CH group per
length unit is removed on each zigzag edge, forming a regular pattern of coves
which controls their electronic structure. Based on three structural parameters
that unambiguously characterize the atomistic structure of ZGNR-C, 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-C with well-defined electronic structure.

Mesoscale and Nanoscale Physics;Materials Science