Visualizing strongly-correlated electrons with a novel scanning tunneling microscope

Materials with strongly correlated electrons show some of the most mysterious and exotic phases of quantum matter, such as unconventional superconductivity, quantum criticality and strange metal phase. In this thesis, we study strongly-correlated electron materials using spectroscopic-imaging scanning tunneling microscopy. We first describe the design and construction of a novel, ultra-stiff, scanning tunneling microscope that is optimized to have the high signal-to-noise ratio required to study these materials. We then present the discovery of the melting of the Mott insulating phase in the iridate Sr2IrO4 upon electron doping, that results in the formation of puddles of pseudogap and charge order. This is striking similar to the cuprate unconventional superconductors and for the first time we show the universality of these phenomena using scanning tunneling microscopy. We moreover discuss the effect of electric field penetration in a poorly conducting sample, and how this affects STM measurements on lightly doped Mott insulators in general. Finally, we show quasiparticle interference measurements on the correlated metal Sr2RhO4, and we discuss its comparison with photoemission results. Quantum Matter and Optic