Graphene nanoribbons (GNRs) have been a very promising candidate for nanoelectronic devices because of their tunable electronic structure with varying width and edge termination. We have shown that semiconducting GNRs of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for topological invariants of armchair GNRs and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants. We also present the calculated topological invariant of GNRs of other edge shapes such as cove-edged and chevron GNRs. Through the topological concept, we are able to design a GNR superlattice that hosts a one-dimensional array of topological interface states, thus generating GNR structure with tunable band gap and bandwidths. Finally, we show that the synthesized boron-doped armchair GNR has strong interaction with the underlying gold substrate, which modifies the properties of boron dopant states according to their symmetries. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

This work is supported by the National Science Foundation, the NSF Center for Energy Efficient Electronics Science the Department of Energy, and the Office of Naval Research under the Muri Program. Computational resources have been provided by DOE at Lawrence Berkeley National Laboratory's NERSC facility and the NSF through XSEDE resources at NICS.