Topological states in engineered atomic lattices

Topological materials exhibit protected edge modes that have been proposed for applications in, for example, spintronics and quantum computation. Although a number of such systems exist, it would be desirable to be able to test theoretical proposals in an artificial system that allows precise control over the key parameters of the model. The essential physics of several topological systems can be captured by tight-binding models, which can also be implemented in artificial lattices. Here, we show that this method can be realized in a vacancy lattice in a chlorine monolayer on a Cu(100) surface. We use low-temperature scanning tunnelling microscopy (STM) to fabricate such lattices with atomic precision and probe the resulting local density of states (LDOS) with scanning tunnelling spectroscopy (STS). We create analogues of two tight-binding models of fundamental importance: the polyacetylene (dimer) chain with topological domain-wall states, and the Lieb lattice with a flat electron band. These results provide an important step forward in the ongoing effort to realize designer quantum materials with tailored properties.