Topological insulators (TIs) are novel states of matter that possess an insulating bulk while hosting low-dimensional conducting boundary states. This behavior emerges as a result of a non-trivial Berry phase encoded in the symmetry of bulk electronic wavefunctions. Over the past decade many experimental and theoretical studies have demonstrated the existence of 2D and 3D TIs, but there has been less exploration into the role of topology in 1D materials. In 2017 T. Cao et al.1 predicted the existence of non-trivial topological phases in quasi-1D graphene nanoribbons (GNRs) and suggested that 0D gapless states should exist at the interface between GNRs having different topological classifications. I will discuss our recent experimental confirmation of this prediction.2 I will show how recent developments in bottom-up synthetic techniques can be used to fabricate atomically-precise graphene nanoribbons with well-defined topology, allowing us to combine topologically trivial and non-trivial GNRs to form 0D symmetry-protected interface states. By carefully positioning such states at precise locations along the GNR backbone we are able to control their hybridization and construct new tailor-made 0D and 1D forms of matter. I will discuss our progress at characterizing these new topological systems using scanned probe microscopy techniques.
 T. Cao, F. Zhao & S. G. Louie Phys. Rev. Lett. 119, 076401 (2017)
 D. J. Rizzo, G. Veber, T. Cao, C. Bronner, T. Chen, F. Zhao, H. Rodriguez, S. G. Louie, M. F. Crommie & F. R. Fischer Nature 560, 204 (2018)