In condensed matter systems electron-electron interactions, negligible in everyday metals, can dramatically alter the electronic behavior of the system. Examples of such altered behavior include... Show moreIn condensed matter systems electron-electron interactions, negligible in everyday metals, can dramatically alter the electronic behavior of the system. Examples of such altered behavior include high-temperature superconductivity and modulation of the electron density. A common feature of this correlation driven behavior is the tendency of the spatial electronic structure to vary on the nanometer scale. In this thesis we explore the nanoscale variation of the electronic structure of various correlated electron systems. We use the wave-like oscillations in the electron density of states to probe fundamental properties of the system providing insights into when various experimental probes disagree with each other. Turning our attention to high-temperature superconductors we find that close to the transition between superconductor and metal a granular superconductor emerges, small nanoscale patches of superconductivity interlaces with a metallic matrix. A careful examination of the wave-like oscillations hints at the presence of spatial ordering of the electrons. Finally we study how the presence of strong interactions can alter the way electrons flow through a material such that concepts usually reserved for everyday fluids become relevant. Show less
This thesis described the development of novel scanning tunneling microscopy techniques to investigate strongly correlated electronic states in quantum matter.
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... Show more 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. Show less
This thesis involves excitonic physics in bilayers of strongly correlated electron materials. The fermionic bilayer extended Hubbard model is studied by means of mean field theory and Determinant... Show moreThis thesis involves excitonic physics in bilayers of strongly correlated electron materials. The fermionic bilayer extended Hubbard model is studied by means of mean field theory and Determinant Quantum Monte Carlo simulations. A bosonic low-energy effective theory is developed, called the exciton t-J model. The phase diagram and the elementary excitations of this model are investigated. Surprisingly, the excitons are predicted to exhibit Ising confinement physics in the antiferromagnetic phase. In the exciton superfluid phase the magnetic triplon modes borrow kinetic energy from the excitons. Show less
