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 the nature and number of the zero-mode edge states of finite-length AGNRs and their structure, topological invariants, and winding number. This allows us to rationalize the design of AGNR heterojunctions and superlattices with tailored phases. We show how the choice of widths, interface coupling geometry, and boundaries determines the emergence of topological states following patterns that depend on the structure and family of the constituent AGNRs. Furthermore, we prove that quantum-well-like states confined in one of the constituent ribbons develop in all the AGNR junctions irrespective of their trivial or topological character. The bipartite nature of the honeycomb lattice is determinant for the topological properties of the junctions: their electronic states can be topologically trivial or nontrivial depending on subtle differences at the boundaries of the ribbons.
Spanish MINECO under Grant No. PGC2018-099199-B-I00 and the European Union structural funds and the Comunidad Autónoma de Madrid (CAM) NMAT2D-CM Program (S2018-NMT-4511). M.C.M. acknowledges financial support of Spanish MINECO under Grant No. RTI2018-097895-BC41 and the FEDER Program of the European Union.