In chapter 3 the energy states of Bismuth Selenide (Bi2Se3) nanoplatelets were investigated in the STM. The nanoplatelets were synthesized in the laboratory in such a way that they are only a few nanometres in thickness. It was shown that the states at the top and the bottom of the material cancel each other out when the platelets are thin enough. Using the location specific techniques of the STM, it was shown that only a single state remains at the edge of the platelet, which could be visualized as a bright ring around the entire platelet as shown in figure 7.1b. Two different theoretical models were then used to model the electronic structure of the platelets and explain the experimental findings. The robustness of these edge states in Bi2Se3 nanoplatelets against disorder, an applied magnetic field, and magnetic adsorbents was investigated in chapter 4. By looking at nanoplatelets with defects and structural irregularities it was shown that the edge state is very robust against disorder. Moreover, even a 5 Tesla magnetic field doesn’t break the state. However, when Mn atoms are deposited on the platelets, the state can be broken. Chapter 5 describes the creation of quantum corrals by manually positioning Carbon Monoxide (CO) molecules on a copper surface. When placed in a circle or a square these electron-repelling molecules confine the electrons of the copper surface. As a result, an artificial atom is created, a square artificial atom can be seen in figure 7.1c. Such artificial atoms are then subjected to a magnetic field, and it is investigated in how far this affects the electronic states. Theoretically it is shown that there are two effects that split the energy states: the Zeeman effect and the Lorentz force. Experimentally it was impossible to replicate these results The last project is described in chapter 6 of this thesis and focusses on dopant atoms in a semiconductor, Gallium Arsenide (GaAs). It is shown how the STM can be used to determine the electronic properties of single dopants. Moreover, we investigated to what extent such dopants can be used to build artificial structures (like the ones in chapter 5) and how the height of the tip can be used to research the effect of a magnetic field on the tunnelling probability through the GaAs surface. Especially the last part of the research shows an unexpected result with the STM tip behaving differently depending on the direction of the magnetic field ramps between -0.5T and 0.5T, as shown in figure 7.1d. This difference couldn’t be explained with the measurements in this work but shows how there will always remain scientific questions to be answered.