Patterning atomic flatland: Electronic lattices crafted atom by atom

‘What would happen if we could arrange the atoms one by one the way we want them?’ (Feynman, 1959) Sixty years after this question was posed, we shine more light on the possibilities provided by the ability to move individual atoms or molecules with atomic precision. In a scanning tunneling microscope, adsorbed carbon monoxide molecules can be moved on an ultraflat copper (111) crystal using an atomically sharp tip. The surface-state electrons of Cu(111), forming a 2D electron gas, are repelled by the carefully positioned CO molecules. In this way, the electrons are forced into designated 2D lattice geometries. Inspired by the work by Gomes et al., who corralled the electrons into a honeycomb geometry, we designed and realized several lattice geometries with tailored electronic properties. After crafting the electronic lattices, we characterized the energy- and spatially resolved density of states using scanning tunneling spectroscopy. The thesis presents the platform of CO on Cu(111) as a testbed that facilitates the realization and characterization of lattices beyond existing materials. Each chapter describes a different artificial electronic lattice. First, we describe the assembly of a Lieb lattice and the observation of its characteristic signature of a Dirac cone intersected by a (nearly) flat band. Next, we modify the Lieb lattice to demonstrate the realization of p-orbital bands in artificial electronic lattices. We create a Sierpiński fractal triangle and reveal that the electronic wave functions inherit a dimension of ~1.58. We continue with the realization of a higher-order topological insulator, the 2D breathing Kagome lattice, and observe topologically protected 0D corner states. Finally, we describe localized excess charges in an electronic 2D SSH lattice. We show that the platform of CO on Cu(111) is a versatile electronic quantum simulator in which the lattice geometry, the orbital degree of freedom, the dimension, the topology and the localized excess charge can be tuned. The approach to design artificial electronic lattices presented in this thesis can be transferred to lattices created lithographically for planar semiconductor electronics