| Over the past twenty-five years, condensed matter physics has been developing materials with novel electronic characteristics for a wide range of future applications. Two research directions have shown particular promise: topological insulators, and high temperature copper based superconductors (cuprates). Topological insulators are a newly discovered class of materials that can be manipulated for spintronic or quantum computing devices. However there is a poor spectroscopic understanding of the current topological insulators and emerging topological insulator candidates. In cuprate superconductors, the challenge lies in raising the superconducting transition temperature to temperatures accessible in non-laboratory settings. This effort has been hampered by a poor understanding of the superconducting mechanism and its relationship with a mysterious pseudogap phase. In this thesis, I will describe experiments conducted on topological insulators and cuprate superconductors using scanning tunneling microscopy and spectroscopy, which provide nanoscale spectroscopic information in these materials.;First, I will describe experiments on the purported topological Kondo insulator SmB6, where a topological surface state is expected to emerge from a strongly correlated hybridization gap. I used a spectral decomposition technique and temperature dependent spectroscopy to measure and observe the opening of the hybridization gap, and find evidence for a topological surface state. I will then describe experiments performed on the topological insulator Bi2-xFexSe3, where I observed the scattering of surface states to surprisingly high energies. Models using density functional theory show that the interaction of the trivial and topological surface states could provide a route towards future topological insulator devices.;I then discuss two experiments performed on the Bi-based cuprates. In the first experiment, I imaged a static charge density wave that, in conjunction with bulk-sensitive probes, reconciles observations of surface and bulk charge ordering in the cuprates over the past twenty years. In the second experiment, I validated previous observations of an electronic nematic order in the pseudogap phase using high spatial-resolution spectroscopy. Together, the work on the cuprates provides insight into the nature of the pseudogap phase, which we find to be characterized by broken symmetries and charge ordering. |
