Materials science

Surface states

Geometry

Quantum

Combinatorics

Physics

Graphene nanoribbons

Scanning tunneling spectroscopy

Topological order

Scanning tunneling microscope

Nanotechnology

Topology (electrical circuits)

Mathematics

Topological insulator

Quantum mechanics

Graphene

Electronic band structure

Band gap

Surface (topology)

Condensed matter physics

Superlattice

Nature

Topological insulators are an emerging class of materials that host highly robust in-gap surface or interface states while maintaining an insulating bulk1,2. Most advances in this field have focused on topological insulators and related topological crystalline insulators3 in two dimensions4–6 and three dimensions7–10, but more recent theoretical work has predicted the existence of one-dimensional symmetry-protected topological phases in graphene nanoribbons (GNRs)11. The topological phase of these laterally confined, semiconducting strips of graphene is determined by their width, edge shape and terminating crystallographic unit cell and is characterized by a                                                                   $${{\mathbb{Z}}}_{2}$$                                                                     invariant12 (that is, an index of either 0 or 1, indicating two topological classes—similar to quasi-one-dimensional solitonic systems13–16). Interfaces between topologically distinct GNRs characterized by different values of                                                                   $${{\mathbb{Z}}}_{2}$$                                                                     are predicted to support half-filled, in-gap localized electronic states that could, in principle, be used as a tool for material engineering11. Here we present the rational design and experimental realization of a topologically engineered GNR superlattice that hosts a one-dimensional array of such states, thus generating otherwise inaccessible electronic structures. This strategy also enables new end states to be engineered directly into the termini of the one-dimensional GNR superlattice. Atomically precise topological GNR superlattices were synthesized from molecular precursors on a gold surface, Au(111), under ultrahigh-vacuum conditions and characterized by low-temperature scanning tunnelling microscopy and spectroscopy. Our experimental results and first-principles calculations reveal that the frontier band structure (the bands bracketing filled and empty states) of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This manifestation of non-trivial one-dimensional topological phases presents a route to band engineering in one-dimensional materials based on precise control of their electronic topology, and is a promising platform for studies of one-dimensional quantum spin physics. A topologically engineered graphene nanoribbon superlattice is presented that hosts a one-dimensional array of half-filled, in-gap localized electronic states, enabling band engineering.

Topological band engineering of graphene nanoribbons