  Topological materials exhibit protected edge modes that have been proposed
for applications in for example spintronics and quantum computation. While 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 tunneling microscopy (STM) to fabricate such lattices
with atomic precision and probe the resulting local density of states (LDOS)
with scanning tunneling 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, featuring a lattice
pseudospin 1 system with a flat electron band. These results provide the first
steps in realizing designer quantum materials with tailored properties.
