Abstract: Cuprate superconductors present a major challenge in condensed matter physics not only due to their electron correlations but also due to their complex crystal structure. Complex crystal structures (e.g., various cations at various lattice positions) demand the utmost care when being synthesized. Molecular beam epitaxy is known to be the foremost versatile tool and technique that allows for the synthesis of such materials without the need to compromise on impurity phases.

First, I introduce our custom-designed molecular beam epitaxy equipment, which is powered by e-guns, not effusion cells, and controlled by electron impact emission spectroscopy. After discussing several material systems, I present high-magnetic-field quantum oscillation data on films synthesized by our molecular beam epitaxy systems. Furthermore, I show results on the charge-ordering mechanism using resonant elastic X-ray scattering. These data support the notion that the appearance of superconductivity in cuprate superconductors is tied to the coordination of the copper in these systems. I will conclude with an outlook that the top of the superconducting transition temperature in cuprate superconductors has not yet been reached.