| Strongly correlated electrons and spin-orbit interaction have been the two major research directions of condensed matter physics in recent years. The discovery of high temperature superconductors in 1986 not only brought excitement into the field but also challenged our theory on quantum materials. After almost three decades of extensive study, the underlying mechanism of high temperature superconductivity is still not fully understood, the reason for which is mainly a poor understanding of strongly correlated systems. The phase diagram of cuprate superconductors has become more complicated throughout the years as multiple novel electronic phases have been discovered, while few of them are fully understood. Topological insulators are a newly discovered family of materials bearing topological non-trivial quantum states as a result of spin-orbit coupling. The theoretically predicted topological Kondo insulators as strongly correlated systems with strong spin-orbital coupling make an ideal playground to test our theory of quantum materials.;Scanning tunneling microscopy (STM) is a powerful technique to explore new phenomena in materials with exotic electronic states due to its high spacial resolution and high sensitivity to low energy electronic structures. Moreover, as a surface-sensitive technique, STM is an ideal tool to investigate the electronic properties of topological and non-topological surface states. In this thesis, I will describe experiments we performed on high temperature superconductors and topological Kondo insulators using STM.;First, I will describe our experiments on a Bi-based high temperature superconductor Bi2Sr2CuO6+delta. The quasiparticle interference technique uncovers a Fermi surface reconstruction. We also discovered the coexistence of Bogoliubov quasiparticle and pseudogap state at the antinodes. Afterwards, I will discuss our discovery of d-form factor density wave in the same material, showing the omnipresence of d form factor density wave above and below the Fermi surface reconstruction. The relation between the d-form factor density wave and the pseudogap state is discussed.;Second, I will describe our experiments on topological Kondo insulator SmB6 where spin-orbit coupling plays an important role in the strongly correlated electron system. I will present the spectroscopic evidence of Kondo hybridization based on a spectral decomposition technique. I will introduce a dimension reduction method in the fitting procedure to reduce the computation time by two order of magnitude. I will also discuss the possible quasiparticle interference patterns we discovered in SmB6. |
