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Scanning tunneling microscopy is a powerful tool to build artificial atomicstructures even not exist in nature but possess exotic properties. We hereconstructed Lieb lattices with different lattice constants by real atoms, i.e.,Fe atoms on Ag(111) and probed their electronic properties. We find asurprising long-range effective electron wavefunction overlap between Feadatoms as it exhibits a 1/r2-dependence with the interatomic distance rinstead of the theoretically predicted exponential one. Combining controlexperiments, tight-binding and Green's function calculations, we attribute theobserved long-range overlap to be enabled by the surface state. Our findingsnot only enrich the understanding of the electron wavefunction overlap, butalso provide a convenient platform to design and explore the artificialstructures and future devices with real atoms.

Lieb lattices formed by real atoms on Ag(111) and their lattice constant dependent electronic properties