One of the key challenges in the field of electronics is to increase the performance of devices while reducing energy consumption. Today’s electronic devices rely on semiconductors, such as silicon. However, as we approach the physical/ atomic limit of how small these components can be made, new materials and concepts are needed for processing and transferring information in an energy efficient way. This thesis explores possible new concepts by studying how materials behave at the atomic level, where quantum effects come into play. The relationship between atomic structure, electronic structure, and dimensionality is studied using a Scanning Tunneling Microscope (STM). The STM can resolve surfaces with atomic resolution and link structural features to the local electronic properties, making it a powerful tool to study quantum phenomena. Moreover, the STM can move single atoms with nanoscale precision, allowing for the construction of atomic structures by design. These quantum simulators mimic the behavior of real materials and enable the study of quantum effects in a controlled way. The research presented in this thesis follows two paths to enhance our understanding of low-dimensional quantum materials: studying natural 2D materials like germanene (a material similar to graphene) and creating artificial electronic structures on semiconductor surfaces. Key findings include a new quantum simulation platform of thin Ag layers on silicon, the study of atom manipulation on a semiconductor InAs(111)A, a new way to examine so-called topological edge modes in one-dimensional atomic chains, and the potential experimental observation of an exotic state of matter in germanene. This work deepens our understanding of quantum phenomena in low-dimensional semiconductors and may help guide future developments in more efficient electronic materials.