The topological properties of graphene nanoribbons (GNRs) have received a significant amount of attention in emerging fields such as spintronics and quantum computing. This study is focused on the energetics and magnetism of symmetry-protected junction state arrays, which are realized in the alternating periodic structures of two topologically different armchair GNRs. We found that the antiferromagnetic states require at least eight unit cells for each segment of the periodic armchair GNRs, where the armchair GNRs whose numbers of carbon atoms in a row are seven and nine are connected with a junction structure. We also found the junction structure that provides more stable antiferromagnetic states. Furthermore, we propose an end (armchair GNRs/vacuum interface) structure to avoid disturbing the global topological properties of the junction state array. This means that if the topological end states (non-trivial phases of the Su, Schrieffer, and Heeger model or Majorana fermions) exist, they are properly formed at the endmost junctions without the requirement for extra effort such as long end extension. We believe that this study can add new guidelines and challenges for realizing graphene-based quantum computing.

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