Tuneable topological domain wall states in engineered atomic chains

Topological modes in one- and two-dimensional systems have been proposed for numerous applications utilizing their exotic electronic responses. The zero-energy, topologically protected end modes can be realized in the Su-Schrieffer-Heeger (SSH) model, which has been experimentally implemented in atomic-scale solid-state structures and in ultra-cold atomic gases. While the edge modes in the SSH model are at exactly the mid-gap energy, other paradigmatic 1D models such as trimer and coupled dimer chains have non-zero energy boundary states. However, these chains have not been realized in an atomically tuneable system that would allow explicit control of the edge modes. Here, we demonstrate atomically controlled trimer and coupled dimer chains realized using chlorine vacancies in the c$(2\times2)$ adsorption layer on Cu(100). This system allows wide tuneability of the domain wall modes that we experimentally demonstrate using low-temperature scanning tunneling microscopy (STM). In the future, these modes may be used to realize well-defined fractional charge states or find applications in exotic quantum devices with atomically well-defined geometries.