Topologically protected edge and confined states in finite armchair graphene nanoribbons and their junctions

Topologically protected edge and junction states, previously predicted, have recently been observed in armchair graphene nanoribbon (AGNR) heterojunctions. Here, via tight-binding-based calculations, we explain the relation between nature number of zero-mode states finite-length AGNRs their structure, topological invariants, winding number. This allows us to rationalize design AGNR heterojunctions superlattices with tailored phases. We show how choice widths, interface coupling geometry, boundaries determines emergence following patterns that depend on structure family constituent AGNRs. Furthermore, prove quantum-well-like confined one ribbons develop all junctions irrespective trivial or character. The bipartite honeycomb lattice is determinant for properties junctions: electronic can be topologically nontrivial depending subtle differences at ribbons.