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
