Record-quality two-dimensional electron systems

Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interaction. Many key observations were made in these systems as sample quality improved over the years. However, progress in quality has been stagnant for over a decade. We present a major breakthrough via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our new samples have a world-record mobility of $44\times10^6$ cm$^2$/Vs at an electron density of $2.0\times10^{11}$ /cm$^2$; this is the highest mobility observed in any material. These results imply only $\sim1$ residual impurity for every $10^{10}$ Ga/As atoms. The impact of such low impurity concentration is extraordinary; several new fractional quantum Hall states emerge, and exotic phases such as the $5/2$ state, which is widely believed to be non-Abelian and of potential use for topological quantum computing, and stripe/bubble phases are unprecedentedly robust.