Manipulating building blocks of matter: The quantum simulation of electronic lattice models

Electrons are one of the main building blocks of matter and are for example responsible for conduction of electricity and heat in materials. Usually there are more than 1018 electrons present in a material of one mm3, which means that the quantum mechanical calculations often become too difficult to solve either by hand or by computer simulations. This is why we take another route and use a quantum simulator to simulate other quantum matter. Our quantum simulator is composed of a copper (Cu) surface, a scanning tunneling microscope (STM) and carbon-monoxide (CO) molecules. Using the STM, the CO molecules are positioned in such a way that they confine the electrons on the Cu(111) surface to certain positions, creating an artificial atom. By connecting different artificial atoms, we construct an artificial molecule and measure its electronic properties such as the density of states. In this thesis, we show how to design different artificial molecules by using the muffin-tin and tight-binding model, and we further show the corresponding experimental results. Specifically, we create the Lieb lattice, a fractal Sierpinski lattice, the breathing Kagome lattice and the necklace-diamond chain, which all host interesting and exotic electronic states. We show full control over the s- and p- orbitals, confine electrons in a fractal dimension of 1.58, and create very robust corner zero modes and a novel type of boundary modes that do not decay into the bulk. Our versatile method provides a pathway to explore new types of matter and proves itself as a proper quantum simulator.