Investigating Atomic Scale Disordered Stripes

The high-Tc cuprate superconductors have been studied for 25 years in the search for the mechanism underlying their superconductivity. In the process, experiments learned that the correlated electrons in these materials organize themselves in a variety of patterns. One such pattern is a type of short-range charge modulations that exist both in and outside of the superconducting phase, which has been linked to the cuprate pseudogap phase. In optimal and slightly underdoped Bi2Sr2CuO6+δ this charge order (labeled Q∗) has wavelength ∼ 5a0. A second and, I argue, related order (Q∗∗) has wavelength of ∼ 1.25a0. These modulations are highly disordered and for this reason their nature is not fully understood. In this thesis I use scanning tunneling microscopy (STM) to study the disorder of these charge modulations, as an avenue to understanding the nature of the charge order itself. Locally, the charge modulations have a preferred orientation, with a wavevector pointing along one crystal axis or the other. But globally, there is no preferred direction. Our most striking finding is that the local orientation is the same for th