The scanning tunneling microscope can be used to build and study synthetic systems that cannot be probed by conventional experiments. Carbon monoxide molecules are arranged on the surface of a Cu (111) single crystal one at a time to form potential landscapes that mimic the ionic potential of natural materials by constraining the electrons in the two-dimensional surface state of Cu (111). This control over the potential landscape on a Cu (111) surface simulates quantum systems with great precision.
First, two synthetic rhombic Penrose tiling quasicrystals were assembled, the Penrose vertex model and the Penrose center model, to examine how electronic states change in the presence of quasicrystalline order. While these quasicrystals have been studied extensively through tight-binding simulations and photoemission surveys, the results presented within this thesis reveal patterns in the local density of states of these quasicrystals with unprecedented detail. Here evidence that the electronic behavior at atomic sites in these synthetic quasicrystals depends on both the local potential of the site and the quasiperiodic order of the structure is presented.
Second, the creation of synthetic molecules using quantum corrals of carbon monoxide molecules is detailed. The experimental images of electronic states in these synthetic molecules show a remarkable match to the charge distribution predicted by density functional theory calculations. Additional carbon monoxide molecules were used to directly break the degeneracy in synthetic aromatic hydrocarbons, and then superposition was used to recombine the resulting Kekul'e structures. The weighted recombination of these Kekul'e structures illustrates the dependence of aromatic molecules on the individual Kekul'e structures.
Finally, an attempt to build a synthetic single molecule transistor by controlling the degeneracy of a synthetic molecule is outlined. The change in the molecule was directly imaged using tunneling spectroscopy, and quasiparticle scattering was utilized to visualize an electronic connection between the source and drain of our prototype single molecule transistor.
Taken together, the results in this thesis demonstrate excellent control over electronic states in simulated quantum systems.