Real-Space Properties of Topological and Correlated Materials

Topological superconductors have been theorized to exhibit novel electronic states known as Majorana states. These states have interesting non-Abelian braiding statistics, which, along with their protection by the topological phase, make them prime candidate states for robust quantum computing. Due to the bulk-boundary correspondence in topological materials, these states are exhibited at the boundaries of materials making real-space probes, such as scanning tunneling spectroscopy (STS) necessary for their characterization. In this dissertation, I discuss the emergence of topological superconductivity in Fe/Re(0001)-O(2X1) as evidenced by STS measurements and compare with theory. I discuss tuning the dimension of generic topological superconductors, which may open the door to furthering the capabilities of engineering Majorana states. I describe a new model of topological superconductivity in FeSe0.45Te0.55. Finally, I examine the real-space probe shot-noise scanning tunneling spectroscopy using the Kondo effect as a testbed.