Quantum coupling of topological junction states in armchair graphene nanoribbon structures

Connecting armchair graphene nanoribbons in series generates topological junction states at the interface when the topology class is not matched due to their difference in the width. The number of such states is investigated for the systems where multiple nanoribbon junctions are mutually coupled quantum-mechanically in two manners. (1) Nonidentical junctions are asymmetrically series-connected. (2) The nanoribbon structures contain parallel paths. It is shown for the asymmetric structures that unpaired states are present at the Dirac point in addition to the paired states that appear away from the Dirac point. The topology class is not established for the individual narrow-wide interfaces in the situation of the parallel paths. The total winding number that provides the number of the topological states is given for the whole junction hosting the parallel paths. Furthermore, the overlap of the topological zero-energy states when the above nanoribbon structures are repeated periodically as superlattices is found to produce no Bloch mode at the Dirac point.