Lieb Lattices Formed by Real Atoms on Ag(111) and Their Lattice Constant-Dependent Electronic Properties

Scanning tunneling microscopy is a powerful tool to build artificial atomic structures that do not exist in nature but possess exotic properties. In this study, we constructed Lieb lattices with different lattice constants by real atoms, i.e., Fe atoms on Ag(111), and probed their electronic properties. We obtain a surprising long-range effective electron wavefunction overlap between Fe adatoms as it exhibits a \frac1r^2 dependence with the interatomic distance r instead of the theoretically predicted exponential one. Combining control experiments, tight-binding modeling, and Green's function calculations, we attribute the observed long-range overlap to being enabled by the surface state. Our findings enrich the understanding of the electron wavefunction overlap and provide a convenient platform to design and explore artificial structures and future devices with real atoms.